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Chapter 3: Q. 21 (page 260)

Find the possibility graph of its derivative f'.

Short Answer

Expert verified


The possibility graph of its derivative f' is

Step by step solution

01

Step 1. Given

The given information is

02

Step 2. Explanation

From the above graph the function is decreasing on (- ∞, 0) where f^ prime <0 and increasing at (0, ∞) where f' prime >0 . Therefore, the possible graph of the derivative of above graph is shown below:

The graph of f' prime have roots at x = 0 and x = 2 . The graph of f^ prime should "bounce" off the x axis at x = 2

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Most popular questions from this chapter

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.

f(x)=x2(x-1)(x+1)

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)=ex(x-2)

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=3x-2ex

Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

f(x)=−x3+3x2−7,[a,b]=[−2,3]

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)=1x2+3
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