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Chapter 3: Q. 17 (page 260)

Determine the graph of a function f from the graph of its derivative f'.

Short Answer

Expert verified

The function f is shown in Graph II and its derivative f' is shown in Graph I.

Step by step solution

01

Step 1. Given 

The given two graphs are

02

Step 2. Explanation

The objective is to find one of the graph is shown as a function f and the other is its derivative

Now, to determine the graph of a function f from the graph of its derivative f'.

Observed form the second figure, the function f must be decreasing on the interval (-∞,-1)

and (0.8,2.6), and increasing on the interval (-1,0.8) and (2.6,∞).

So, the one of the possible sketch of a function f that has these characteristics is shown in the graph II.

Therefore, the graph I indicates the derivative of a function f.

Hence, the function is shown in Graph II and its derivative f' is shown in Graph I

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Most popular questions from this chapter

Find the possibility graph of its derivative f'.

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)=2x,[a,b]=[0,3]

Determine whether or not each function fsatisfies 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)=tanx,[a,b]=[-π,π].

Find the critical points of the function

f'(x)=1+x2-4

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)=1x-12x-2
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