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Chapter 3: Q. 54 (page 261)

For each sign chart for f'in Exercises 51-56, sketch possible graphs of both f'and f. On each sign chart, unlabeled tick-marks are locations where f'xis zero and x-values where f'xdoes not exist are indicated by tick-marks labeled 鈥淒NE.鈥�

Short Answer

Expert verified

The possible picture off' is,

The possible picture off is,

Step by step solution

01

Step 1. Given information

On the sign chart, unlabeled tick-marks are locations where f'xis zero and x-values where f'xdoes not exist are indicated by tick-marks labeled 鈥淒NE.鈥�

02

Step 2. From the sign chart, it is cleared that the value of f' is positive at -2,0 and 0,2 and negative at -∞,-2 and 2,∞.

The possible picture off' is,

03

Step 3. As f' is positive on -∞,0 and 5,∞, f is increasing on -∞,0 and 5,∞.

As f'is negative on 5,鈭�, fis decreasing on 5,鈭�.

The possible picture of fis,

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Most popular questions from this chapter

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)=cos2(x)

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

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).

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

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