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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

Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

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→0definition of the derivative and then

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

25.f(x)=1x,x=-1

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that passes through the point (3,2)and is parallel to the tangent line to f(x)=1x at x=-1.

Instead of choosing small values of h, we could have chosen values of z close to c. What limit involving z instead of h is equivalent to the one involving h?
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