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Chapter 3: Q. 25 (page 261)

Find the possibility graph of its derivative f'.

Short Answer

Expert verified

The possibility graph of its derivative f' is

Step by step solution

Step 1. Given

The given information is

Step 2. Calculation

From the above graph, f'>0 at (3, $\infty$ ); the function is increasing from (3,0); the graph f'<0 at (-0,1) and (1,3) where the function is decreasing.

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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(0) = 5;

f(−2) = −3 and f '(−2) = 0;

f '(1) does not exist;

f' is positive only on (−2, 1).

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

f is continuous and defined on R;

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

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

Use a sign chart for $f^{'}$ to determine the intervals on which each function $f$ is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

$l n (x^{2} + 1)$

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 $f, f', a n d f'',$ and examine any relevant limits so that you can describe all key points and behaviors of f.

$f (x) = x^{2} + 3 x$

Use a sign chart for $f^{'}$ to determine the intervals on which each function $f$ is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

role="math" localid="1648368106886" $f (x) = s i n (\frac{π}{2} x)$

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Find the possibility graph of its derivative f'.

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

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Most popular questions from this chapter

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