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Chapter 3: Q. 21 (page 275)

In Exercises 21–28, graphs of f, f', or f'' are given. Whichever is shown, sketch graphs of the remaining two functions. Label the locations of any roots, extrema, and inflection points on each graph.

Short Answer

Expert verified

Roots of f' are x=0,4 and graph of f' is the following.

The root of f'' is x=2and the graph off' is the following.

Step by step solution

01

Step 1. Given information. 

The given graph of f is the following.

02

Step 2. Graph of f'.

Graph of f state that the f' is increasing on the interval -∞,0.

f' is decreasing on the interval 0,4.

f' is increasing on the interval 4,∞.

f' have horizontal tangent at x=0,4. so roots of f' arex=0,4.

03

Step 3. Graph of f''.

Graph of f' state that f''is decreasing on the interval-∞,2.

f'' is increasing on the interval2,∞.

f'' have horizontal tangent at x=2,so root of f'' isx=2.

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Most popular questions from this chapter

Sketch careful, labeled graphs of each function f in Exercises 63–82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

f(x)=(x−2)(x+2)

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=x3+4x2+4x-5

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

fx=3x4+8x3-18x2

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points .

fx=In2xx
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