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Chapter 3: Q. 18 (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

Observed form the second figure, the function f must be decreasing on the interval (- 鈭�, - 1) and (1,3), and increasing on the interval (-1,1) and (3, 鈭�) .

So, the one of the possible sketch of a function f that has these characteristics is shown in the graph 11.

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

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

As we can find the local extremum using first derivative. From the above graph I, the function is decreasing at (-2,0) and (2,4) where f' <0 and increasing on (0,2). Therefore, the graph Il indicates the derivative of a function f.

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Most popular questions from this chapter

For each graph of f in Exercises 49鈥�52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

For each graph of f in Exercises 49鈥�52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

Sketch the graph of a function f with the following properties:

f is continuous and defined on R;

f(0) = 5;

f(鈭�2) = 鈭�3 and f '(鈭�2) = 0;

f '(1) does not exist;

f' is positive only on (鈭�2, 1).

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

Determine whether or not each function f in Exercises 53鈥�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 鈭� (a, b) that satisfy the conclusion of the Mean Value Theorem.

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