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1How to find the point where the graph has horizontal tangent lines using derivatives

2Find the horizontal tangent line y=x/( square root of 2x-1) [1]

3 Implicit differentiation [2]

4 Where does the curve y = x 4 2 x 2+2 have any horizontal tangents?A. 0,2,1,1 and 1,1B. 0.0, 1.1 and 1.3C. 3,4,2,1 and 1,4D. 0,4,3,1 and 2,4 [3]

5 Determine the points where the graph of the function has a horizontal tangent line. f(x) = x2 [4]

6How to draw the graph of y = 3^x − 2x with a horizontal tangent line [5]

7 Derivative and Tangent Line [6]

8SOLVED: Determine the point(s) where the graph of f(x)=(x)/(√(2 x-1)) has a horizontal tangent. [7]

9 The rate of change of a function [8]

10 stationary points [9]

11 Numeracy, mathematics and statistics [10]

12 Where does the curve y = x 4 2 x 2+2 have any horizontal tangents?A. 0,2,1,1 and 1,1B. 0.0, 1.1 and 1.3C. 3,4,2,1 and 1,4D. 0,4,3,1 and 2,4 [11]

133.2: The derivative as a function [12]

14Find the equation for a line tangent to a curve at a given point [13]

15Find the tangent to the graph of the function which is perpendicular to the line [14]

16 Horizontal asymptotes and intersections [15]

17 Sources

### How to find the point where the graph has a horizontal tangent line using derivatives

How to find the point where the graph has a horizontal tangent line using derivatives

How to find the point where the graph has a horizontal tangent line using derivatives

### Find the horizontal tangent line y=x/( square root of 2x-1)^{[1]}

Move to the denominator using the negative exponent rule .. Combine numerators over the common denominator.

Differentiate using the Power Rule, which states that it is where .. Differentiate using the Chain Rule, which states that it is where and .

To write as a fraction with a common denominator, multiply by .. Combine the numerators above the common denominator.

### Implicit differentiation^{[2]}

Implicit differentiation, partial derivatives, horizontal tangent lines, and solving nonlinear systems are discussed in this lesson. Consider folium x3 + y3 9xy = 0 from Lesson 13.1

One method of finding the slope is to take the derivative of both sides of the equation with respect to x. When taking the derivative of an expression containing y, treat y as a function of x

Implicit differentiation of folium x3 + y3 9xy = 0 gives .. Note that the expression -9xy is considered a product of two functions and the product rule is used to find its derivative, .

### Where does the curve y = x 4 2 x 2+2 have any horizontal tangents?A. 0,2,1,1 and 1,1B. 0.0, 1.1 and 1.3C. 3,4,2,1 and 1,4D. 0,4,3,1 and 2,4^{[3]}

Solve the equation: dydx=0 (since the slope of the horizontal tangent is zero). The curve y=x4−2×2+2 has horizontal tangents at x=0,1 and −1

### Determine the points where the graph of the function has a horizontal tangent line. f(x) = x2^{[4]}

Determine the points where the graph of the function has a horizontal tangent line. We need to find the points where the graph of the function has a horizontal tangent line.

Determine the points where the graph of the function has a horizontal tangent line. The points where the graph of the function has a horizontal tangent line

### How to draw y = 3^x − 2x with a horizontal tangent line^{[5]}

How to draw y = 3^x − 2x with a horizontal tangent line. Use MATLAB to find all values of x where the graph of y = 3^x − 2x has a horizontal tangent line

You can plot the tangent line by choosing two x endpoints, like -1 and 1 or whatever, then calculate the y values there and call plot(). Let's say you want the tangent at xp = 0 or whatever

% Define left and right locations for the endpoints of the tangent line. % Point slope formula : (y-yp) = slope * (x-xp), or yp = slope * (x-xp) + yp

### Derivative and Tangent Line^{[6]}

The first derivative of a function is the slope of the tangent line for any point on the function! Therefore, it tells when the function is increasing, decreasing or where it has a horizontal tangent! Consider the following graph: Notice on the left that the function is increasing and the slope of the tangent line is positive

These observations lead to a generalization for any function f(x) that has a derivative on an interval I :. Here are some graphs of each of the observations above!

2) To be a maximum point, the graph must change direction from increasing to decreasing. 3) To be an inflection point, the graph does not change direction

### SOLVED: Determine the point(s) where the graph of f(x)=(x)/(√(2 x-1)) has a horizontal tangent.^{[7]}

Get 5 free video unlocks on our app with the code GOMOBILE. Determine the point(s) where the graph of $f(x)=\frac{x}{\sqrt{2 x-1}}$ has a horizontal tangent.

Determine the point(s) where the graph of the function has a horizontal tangent.. Determine the point(s) where the graph of the function has a horizontal tangent line.

Horizontal Tangent Line Determine the point(s) where the graph of $f(x)=\frac{x}{\sqrt{2 x-1}}$ has a horizontal tangent. So here we have the curve F for X is equal to X divided by the square root of two

### The rate of change of a function^{[8]}

Before we get down to the basics of the derivative of a function, let's review some terminology and concepts. Remember that the slope of a line is defined as the quotient of the difference in y values and the difference in x values

Suppose we get two points \(\left(x_{1},y_{1}\right)\) and \(\left(x_{2},y_{2}\right)\) on the line of a linear function \(y = f(x)\text{.}\) Then the slope of the line is calculated by. We can interpret this equation by saying that the slope \(m\) measures the change in \(y\) per unit change in \(x\text{.}\) In other words, the slope \(m\) provides a measure of sensitivity.

Next, we introduce the properties of two special lines, the tangent line and the secant line, which are relevant to the understanding of a derivative.. Secant is a Latin word meaning to cut, and in mathematics a secant line intersects an arbitrary curve described. at \(y = f(x)\) through two points \(P\) and \(Q\text{.}\) The figure shows two such secant lines of the curve \(f\) to the right and to the left for respectively the point \(P\text{,}\).

### Stationary points^{[9]}

A stationary point or critical point is a point where the gradient of the curve is equal to zero. If a curve has the equation \(y=f(x)\), then at a stationary point we will always have:

horizontal (increasing or decreasing) inflection points.. It is worth pointing out that maximum and minimum points are often called turning points.

each of which is illustrated in the graphs shown here, where the horizontal tangent is shown in orange:. A horizontal inflection point is a stationary point which is either:

### Speaking, mathematics and statistics^{[10]}

A stationary point of a function $f(x)$ is a point where the derivative of $f(x)$ is equal to 0. These points are called "stationary" because the function is neither increasing nor decreasing at these points

The stationary points of a function $y=f(x)$ are the solutions of This repeats in mathematical notation the definition above: "points where the gradient of the function is zero".

Note: all turning points are stationary points, but not all stationary points are turning points. A point where the derivative of the function is zero but the derivative does not change sign is known as an inflection point or saddle point

### Where does the curve y = x 4 2 x 2+2 have any horizontal tangents?A. 0,2,1,1 and 1,1B. 0.0, 1.1 and 1.3C. 3,4,2,1 and 1,4D. 0,4,3,1 and 2,4^{[11]}

Solve the equation: dydx=0 (since the slope of the horizontal tangent is zero). The curve y=x4−2×2+2 has horizontal tangents at x=0,1 and −1

### 3.2: The derivative as a function^{[12]}

– Define the derivative of a given function. – Draw the graph of a derivative function from the graph of a given function.

– Describe three conditions for when a function does not have a derivative.. – Explain the meaning of a higher-order derivative.

If we differentiate a position function at a given time, we get the velocity at that time. It seems reasonable to conclude that knowing the derivative of the function at any point would provide valuable information about the behavior of the function

### Find the equation of a line tangent to a curve at a given point^{[13]}

Sample Question #1: Find the equation of a line tangent to a curve at a given point. Find the equation of the line tangent to the graph of

Therefore, finding the derivative of our equation will allow us to find the slope of the tangent line. Since the two things needed to find the equation of a line are the slope and a point, we would be halfway done.

To achieve this, we simply substitute our x value 1 into the derivative. Our choices are quite limited, since the only point on the tangent line that we know is the point where it intersects our original graph, namely the point .

### Find the tangent to the graph of the function that is perpendicular to the line^{[14]}

Find the tangent to the graph of the function $f (x) = \ln (x-1) ^ 2$ which is perpendicular to the line $p$: $y = \frac{2}{5}x +2$ . I decided $kp = 2/5$ and planted in $kn = -1/kp = -5/2 \to kt = -5/2$

Is this procedure correct and how do I express the tangent equation?

### Horizontal asymptotes and intercepts^{[15]}

– Use the degree of the numerator and denominator of a rational function to determine what kind of horizontal asymptote it will have. – Determine the intercepts of a rational function in factored form.

Remember that the end behavior of a polynomial will mirror that of the leading term. Likewise, the final behavior of a rational function will reflect the relationship between the leading terms of the numerator and denominator functions.

Case 1: If the degree of the denominator > degree of the numerator, there is a horizontal asymptote at [latex]y=0[/latex]. Example: [latex]f\left(x\right)=\dfrac{ 4x+2}{{x}^{2}+4x – 5}[/latex]

### Sources

- https://www.mathway.com/popular-problems/Calculus/554724
- https://education.ti.com/html/t3_free_courses/calculus89_online/mod13/mod13_lesson2.html#:~:text=If%20the%20slope%20is%20zero,the%20denominator%20is%20not%20nul.
- https://byjus.com/question-answer/where-does-the-curve-y-x-4-2x-2-2-have-any-horizontal-tangents-02-1/#:~:text=%2C1 %2C%E2%88%921-,%20kurven%20y%3Dx4%E2%88%922×2%2B2,0%2C1%20og%20%E2%88%921.
- https://www.cuemath.com/questions/determine-the-points-at-which-the-graph-of-the-function-has-a-horizontal-tangent-line-fx-x2-8/
- https://www.mathworks.com/matlabcentral/answers/1660460-how-to-graph-y-3-x-2x-with-a-horizontal-tangent-line
- https://www.mathstat.dal.ca/~learncv/DerInCurve/
- https://www.numerade.com/questions/determine-the-points-at-which-the-graph-of-fxfracxsqrt2-x-1-has-a-horizontal-tangent/
- https://www.sfu.ca/math-coursenotes/Math%20157%20Course%20Notes/sec_Slope.html
- https://www.radfordmathematics.com/calculus/Differentiation/stationary-points/stationary-points.html
- https://www.ncl.ac.uk/webtemplate/ask-assets/external/maths-resources/core-mathematics/calculus/stationary-points.html
- https://byjus.com/question-answer/where-does-the-curve-y-x-4-2x-2-2-have-any-horizontal-tangents-02-1/
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/03%3A_Derivatives/3.02%3A_The_Derivative_as_a_Function
- https://www.varsitytutors.com/precalculus-help/find-the-equation-of-a-line-tangent-to-a-curve-at-a-given-point
- https://math.stackexchange.com/questions/3917391/find-the-tangent-to-the-graph-of-the-function-which-is-perpendicular-to-the-line
- https://courses.lumenlearning.com/waymakercollegealgebra/chapter/horizontal-asymptotes-and-intercepts/

## FAQs

### How do you determine where a function has a tangent line? ›

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

**At what point is the tangent to f x x 2 4x 1 horizontal? ›**

The final answer is **−5 - 5** . The horizontal tangent line on function f(x)=x2+4x−1 f ( x ) = x 2 + 4 x - 1 is y=−5 .

**How do you find a point on a horizontal line? ›**

Horizontal lines have a slope of 0. Thus, in the slope-intercept equation y = mx + b, m = 0. The equation becomes **y = b, where b is the y-coordinate of the y-intercept**.

**What is the tangent point of a function? ›**

A tangent line is **a straight line that touches a function at only one point**. (See above.) The tangent line represents the instantaneous rate of change of the function at that one point. The slope of the tangent line at a point on the function is equal to the derivative of the function at the same point (See below.)

**How do you find the tangent line is horizontal or vertical? ›**

**A horizontal tangent occurs whenever cost = 0, and sint = 0**. This is the case whenever t = π/2 or t = 3π/2. Substituting these parameter values into the parametric equations, we see that the circle has two horizontal tangents, at the points (0,1) and (0,1). A vertical tangent occurs whenever sint = 0, and cost = 0.

**Where does the curve y x4 − 2x2 2 have any horizontal tangents? ›**

The curve y=x4−2x2+2 have horizontal tangents at **x=0,1 and −1**.

**Is the point where the tangent is horizontal or where the first derivative is equal to 0? ›**

**A stationary point** of a function f(x) is a point where the derivative of f(x) is equal to 0. These points are called “stationary” because at these points the function is neither increasing nor decreasing. Graphically, this corresponds to points on the graph of f(x) where the tangent to the curve is a horizontal line.

**What is the slope of a horizontal tangent line? ›**

The slope of a horizontal tangent line is **0** (i.e., the derivative is 0) as it is parallel to x-axis. The slope of a vertical tangent line is undefined (the denominator of the derivative is 0) as it is parallel to the y-axis.

**What is the horizontal formula? ›**

A horizontal line is a line that is parallel to the x-axis of the coordinate plane and its equation is of the form **y = b**, where 'b' is constant, whereas, a vertical line is a line parallel to the y-axis and its equation is of the form x = b, where 'b' is constant.

**What are horizontal tangent values? ›**

The equation has a horizontal tangent **when the slope of the tangent is zero**. The slope of the tangent line to the graph of f(x) is actually f'(x). So when f'(x) = 0 we have a horizontal tangent line (the point where it changes from increasing to decreasing or vice versa).

### What is a horizontal point? ›

In coordinate geometry, a line is said to be horizontal if **two points on the line have the same Y- coordinate points**. It comes from the term “horizon”. It means that the horizontal lines are always parallel to the horizon or the x-axis.

**What is an example of a horizontal line? ›**

A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. **The x-axis** is an example of a horizontal line.

**What is a horizontal line on a graph? ›**

In more simple terms, a horizontal line on any chart is **where the y-axis values are equal**. If it has been drawn to show a series of highs in the data, a data point moving above the horizontal line would indicate a rise in the y-axis value over recent values in the data sample.

**What is a point on the graph where the tangent line is either horizontal or vertical known as? ›**

The geometric interpretation of what is taking place at a **critical point** is that the tangent line is either horizontal, vertical, or does not exist at that point on the curve. Example 1: Find all critical points of .

**What is the slope of the tangent line with a vertical line? ›**

In mathematics, particularly calculus, a vertical tangent is a tangent line that is vertical. Because a vertical line has **infinite slope**, a function whose graph has a vertical tangent is not differentiable at the point of tangency.

**What is the tangent point called? ›**

The point where tangent meets the circle is called **point of tangency**. The tangent is perpendicular to the radius of the circle, with which it intersects. Tangent can be considered for any curved shapes. Since tangent is a line, hence it also has its equation.

**What is horizontal tangent line and vertical tangent line? ›**

Horizontal tangent lines exist where the derivative of the function is equal to 0, and vertical tangent lines exist where the derivative of the function is undefined.

**What is tangent angle examples? ›**

The tangent of an angle is the trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle. Example: In the triangle shown, **tan(A)=68 or 34 and tan(B)=86 or 43** .

**What is the slope of the line tangent to the curve 3y2 − 2x2 6 − 2xy at the point 3 2? ›**

What is the slope of the line tangent to the curve 3y^{2} - 2x^{2} = 6 - 2xy at the point (3, 2)? Summary: The slope of the line tangent to the curve 3y^{2} - 2x^{2} = 6 - 2xy at the point (3, 2) is **4/9**.

**What is the point on the curve y x 2 3x 2 where tangent is perpendicular? ›**

The point on the curve y = x^{2} – 3x + 2 where tangent is perpendicular to y = x is. So, the required point is **(1, 0)**.

### Where does f x 3x 2 6x have a horizontal tangent line? ›

The final answer is **−3 - 3** . The horizontal tangent line on function f(x)=3x2−6x f ( x ) = 3 x 2 - 6 x is y=−3 .

**What is the point at which the tangent to the curve? ›**

A tangent line is a line that touches a curve at a single point and does not cross through it. The point where the curve and the tangent meet is called the **point of tangency**.

**What is the first tangent point of curve? ›**

The starting point of the curve is called 'point of the curve' or 'point of commencement'. The tangent line drawn on a curve at its end is known as Forward tangent. The tangent line drawn on a curve at its starting point is known as the Backward tangent.

**What is the formula of horizontal asymptote? ›**

A horizontal asymptote of a graph is a horizontal line **y = b** where the graph approaches the line as the inputs approach ∞ or –∞. A slant asymptote of a graph is a slanted line y = mx + b where the graph approaches the line as the inputs approach ∞ or –∞.

**How do you write a horizontal tangent line? ›**

Horizontal lines have a slope of zero. Therefore, when the derivative is zero, the tangent line is horizontal. To find horizontal tangent lines, use the derivative of the function to locate the zeros and plug them back into the original equation.

**How do you solve vertical tangent lines? ›**

**How to Find the Vertical Tangent**

- Find the derivative of the function. The derivative (dy/dx) will give you the gradient (slope) of the curve.
- Find a value of x that makes dy/dx infinite; you're looking for an infinite slope, so the vertical tangent of the curve is a vertical line at this value of x.

**At what points is the tangent line horizontal vertical? ›**

A horizontal tangent line means the slope is zero, which means the change in y is zero. Equate dy/dt to 0 and solve for the value of t. A vertical tangent means the slope is infinite and the change in x is zero. Equate dx/dt to zero and solve for the value of t.

**When the tangent line is horizontal What is its slope? ›**

A horizontal tangent is parallel to x-axis and hence its slope is **zero**.

**How do you know if a tangent line is vertical or horizontal? ›**

**Horizontal tangents occur when the derivative equals 0** . Vertical tangents occur when the derivative is undefined.

**What is a vertical tangent line? ›**

In mathematics, particularly calculus, a vertical tangent is **a tangent line that is vertical**. Because a vertical line has infinite slope, a function whose graph has a vertical tangent is not differentiable at the point of tangency.

### What if the slope is horizontal? ›

What is a horizontal line's slope? A horizontal line has no vertical change, so **its slope is zero**.

**What happens if the slope is horizontal? ›**

Zero! This relationship always holds: a slope of zero means that the line is horizontal, and a horizontal line means **you'll get a slope of zero**.

**What is the slope of a horizontal curve? ›**

Slope of Horizontal Lines is **Zero**.