Sketch the graph of a functionf having the following characteristics f(2) f(4) 0 f(x)0 if x > 3 f(3) is defined f'(x)0 if x < 3 "(x)0, if 3 f'(3) does not exist

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: What derivative tests are available for determining the local extreme values of a function ƒ(x, y)?…

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Q: ) The tangent line to y = f(x) at (-5, 2) passes through the point (-7, -5). Compute the following.…

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Q: 1. Using the First Derivative Test, explain why the function f(x) =-2x has no extrema on any open…

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Q: 1 Find the derivative of f(x) = - at x= 3 %3D (Type an integer or a simplified fractic 21 %3D

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Q: How can we use the derivative f'(x) of a function f(x) to determine where the local max(s) and…

A: Given query is to provide the procedure to find local max and min with the use of derivative of a…

Q: Find local maximum or local minimum of f(x)= -sin 2x -x defined on 22

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Q: find the tangent line of f(x)= 3x-4/x+1 at x=0

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Q: The derivative of a certain continuous and differentiable function is given by: y = 3-x - 12-x +9.…

A: For maxima-minima, derivative of the function must be zero. That is,…

Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

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Q: Suppose F(x) is a differentiable function for all real numbers x. Evaluate the following derivative.…

A: We need to find the derivative of the function F(x^4) with respect to x.

Q: The function has only one critical point at x = VIn(a). Use the Second Derivative test to identify…

A: Solve g'(x)=0 to obtain the critical points. Then evaluate g'' at those critical points. If it is…

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: 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: sketch the graph of a function f whose derivative f' has the given description. f'(x) is negative on…

A: The graph of a function f whose derivative f' has the given description. f'(x) is negative on (1, 3)…

Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

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Q: Please help. *Find the equation of the normal line (NL) to the graph f(x)=x³-4x at x = 3. *For…

A: To find the equation of normal line to the curve

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 8

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Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

Q: The function f is defined by f(x)=x/(x+2). What points (x, y) on the graph of f have the property…

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Q: 8. Using the second derivative test, find the maximum and minimum points for the function f(x)-x*…

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Q: 9) Use the second Derivative Test to find all relative extrema. f( x) = - (x + 2)°(x – 4)?

A: Find f'(x) and solve for x by putting f'(x)=0.

Q: 3) (a) Let f(x) = -x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: Use second derivative test, If f(x) = - 4x + 10 then f(x) has a local maximum at the point 3 %3D O r…

A: here we need to find the point at which the function has a local maxima. the solution is following.

Q: ve of the function using the definition of derivative. = V7- x 1 2 7-x n of the function. (Enter…

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Q: 3. Suppose a car travels at a constant rate of 70 kph for 2 hours and travels 55 kph thereafter.…

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

Q: Find an equation of the tangent line to the graph of function f(x): 3 %3D x+5 at the point (2, ).…

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

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Q: At what points are the functions continuous x -X- g(x) = X - 3 y " 5, x = 3

A: Given:  1. 2.

Q: f(x) = ln (1/x^6)

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

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

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

Q: Find f′(x) from f(x)=2x^3−x^2−x+2 using the definition of a derivative. (Do not include "f′(x)=" in…

A: we have to find f'(x) using limit definition of derivative

Q: A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f, the tangent…

A: Given problem:- A nonnegative function f has domain (0, ∞). At each point P(x, y) on the graph of f,…

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

Q: 5. Find f '(x) if f(x) = Vx+3 using the limit definition of the derivative. You must show all steps…

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Q: 1. Sketch a function that has a horizontal tangent line for all values of x. Explain how you arrived…

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

Q: On the interval -2<x<-1/2, the graph of the curve f (x) = 2x° +3x2 - 12x - 7 is: %3D Support answer…

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Q: , (a) Let f(x) = −x²-x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

A: The objective of the question is determine the equation of tangent line to the given function.

Q: 13. Suppose a continuous function f and its derivative f' have values table. Given that f(1) 2, use…

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Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

Q: The function g has first derivative given by g'(x) What is 1+x + x3 the x-coordinate of the…

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Q: Find the point on the line y = – 4x + 2 closest to the point (8, 9). - The function giving the…

A: Given, equation of line : y = -4x +2 And  The point : (8, 9) {outside the line}

Q: The rule of the derivative of a function f is given. Find the location of all local extrema. f'(x) =…

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Q: Find the derivative of the function. show all work y=(x-10)(x^2+2x) all over x^3

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Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A: Given : what is defined as the limit of the ratio of the change in a function to the corresponding…