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Chapter 2: Q. 30 (page 166)

Sketch a graph of the associated slope function f' for each function f.

Short Answer

Expert verified

The graph of slope function is:

Step by step solution

01

Step 1. Given Information

We are given the graph of a functionfand we need to find its associated slope functionf'.

02

Step 2. Finding the slope function

A good place to begin is by marking all the locations on the graph of f where the tangent line is horizontal and thus has slope 0. Thus the associated slope function f' is:

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Most popular questions from this chapter

For each function fgraphed in Exercises 65-68, determine the values of xat which ffails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.

Use (a) the h鈫�0definition of the derivative and then

(b) the z鈫�cdefinition of the derivative to find f'(c) for each function f and value x=c in Exercises 23鈥�38.

24.f(x)=x3,x=1

For each function f(x)and interval a,bin Exercises 81-86, use the Intermediate Value Theorem to argue that the function must have at least one real root on a,b. Then apply Newton鈥檚 method to approximate that root.

f(x)=x3+1,a,b=-2,1

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=x+45

Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra

f'(x)=3x5-2x2+4;f(0)=1
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