In Exercises 21-24, sketch the graph of a function f that has the listed characteristics. 21. f(1) = 2, f'(1) = 0, f'(3) = 2 22. f'(-3) = 0, f'(-1) = 0, f'(2) = 0 23. f(-1) = 2, f'(-1) = 3, ƒ(1) = -2, f'(1) = 3 24. f'(-2) = 2, f'(0) = 1, f(1) = –5

Q: Can a function have an inflection point at a critical point? Explain

A: Show that: Can a function have an inflection point at a critical point?

Q: What is the critical point of this function?

A: Critical points are that points where derivative is zero

Q: 9) If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Since you have asked multiple question in a single request, we would be answering only the first…

Q: Example: Sketch pictures of some functions that would not have a derivative at x = 2.

A:

Q: Let F(x) be a function whose derivative F' (x) = f(x) is graphed below: -3 -2 3 6 --1 = -11.75,…

A:

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: In Exercises 20–21, find a formula for the derivative using the power rule. Confirm it using…

A: NOTE: Refresh your page if you can't see any equations. . take derivative (using power rule)

Q: 1. If the first derivative is zero and the second derivative is positive, what can be concluded in…

A:

Q: Sketch a potential f(x) given the following graph of the first derivative f'(x). Explain you…

A:

Q: How do I differentiate this function using the chain rule: f(x)=[x^2/sin(x)]^6

A: Given,           The function is fx=x2sinx6.

Q: Which defines as the process of finding the derivative of a function? *

A: Here, to tell which defines as the process of finding the derivative of a function.

Q: Page < 11. Use f'(x) = lim x+h)-f(x) to find the derivative of f(x) = x² + 3.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: why setting the derivative of a function equal to zero allows us to find the maximum or minimum…

A:

Q: Use the alternate definition, lim Ax)-Aa) to determine the instantaneous rate of X- a change of Ax)…

A:

Q: What information about a graph can be found from the second derivative?

A: What information about a graph can be found from the second derivative?

Q: Suppose that the function y in the Derivative Product Rule has a constant value c. What does the…

A: Derivative product rule:The derivative product rule for the functions x and y is given by,

Q: In Exercises 17–20, the linear function. use the limit definition to calculate the derivative of

A: Given function is fx=12. Derivative of function fx using the limit definition is given as:…

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: theoretically define what is the derivative of a transform and what is its function

A: Given data is : Define what is derivative.

Q: 2. Write an example of a function whose derivative can be found by using the following rules: Power…

A:

Q: Sketch the graph of the floor function f(x) = x+ 1| over the interval [-3, 3) %3D Show your work

A:

Q: Define wronskian of Two Functions?

A: Wronskian of two function: Let f(x) and g(x) be two differentiable functions, then wronskian of f(x)…

Q: pn, sketche 40 7- 1- -3 -1 -2 -3 hu r

A:

Q: Chapter 2.1 (The limit definition of derivative needs to be used Find the derivative of f(x)=z² – 5z

A:

Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx *please explain step by…

A:

Q: Explain the rule of maximum and minimum using Derivatives with an example?

A:

Q: If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Given :   If a function is decreasing with an upward concavity To find : the function's first two…

Q: 3. Give a sketch of the function using the information provided in the given derivative map.

A: we can see graph

Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

Q: Sketch the graph of f. fx) 5 fx) 5 4 3 2 2 1 1 3 4 4 -3 -2 -1 1 3 4 -4 -3 -2 -1 -1 -1 f(x) f(x) 5, 3…

A:

Q: 5. What is the definition of the derivative of a function f(x) ?

A:

Q: Sketch a graph of a function whose derivative is zero at exactly two points. Explain how you found…

A: Sketch the graph of a function whose derivative is zero at exactly two points which means we can…

Q: In Exercises 67–73, estimate derivatives using the symmetric difference quotient (SDQ), defined as…

A:

Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

A:

Q: 2. Use an example to show how to use the First Derivative Test for critical points

A:

Q: Compute f'(3) using the limit definition of derivative if f

A: Given: f(x)=6x2f'(3)

Q: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

A:

Q: In Exercises 41 – 46, confirm your results with a graphing utility. 41. For the function f(x)= x³ +…

A: We have to solve

Q: Compute the average rate of change of f(x) = x2-1/x on the interval of [2,4]. Please show me each…

A:

Q: determine maximums and minimums by the Second Derivative Test, we differentiate y"=72 / (2-8)3…

A: topic  - local maxima and minima

Q: In Exercises 31–38, find the slope of the graph of the function at the indicated point. Use the…

A:

Q: Explain derivatives on optimization ?

A: Topic:- derivatives

Q: ______ provide a means to predict the value of a function at one point in terms of the function…

A: Given: Let us consider the given statement, "______ provide a means to predict the value of a…