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Chapter 3: Q. 20 (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

The objective is to sketch a possible graph of its derivative f".

From the above graph, the function f(x) is increasing in the interval (-3.2,-2.2) and

(-1,1.5)

So. f'(x) > 0 is in the interval (-3.2,-2.2) and (-1,1.5)

From the above graph, the function f(x) is decreasing in the interval (-2.2,-1) and

(1.5,2.1)

f'(x) < 0 in the interval (-2.2,-1) and (1.5,2.1)

f'(x)=0 at x = -2.2, x=-1 and x = 1.5.

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Most popular questions from this chapter

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

f is continuous and defined on R;

f has critical points at x = 鈭�3, 0, and 5;

f has inflection points at x = 鈭�3, 鈭�1, and 2.

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

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)=xx2+4

Use the definitions of increasing and decreasing to argue that f(x)=x4 is decreasing on (鈭�鈭�,0] and increasing on [0,鈭�). Then use derivatives to argue the same thing.

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)=2x3鈭�9x2+1
See all solutions

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