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Chapter 3: Q. 22 (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

Step 1. Given

The given information is

Step 2. Explanation

From the above graph the function is decreasing on (- ∞, 0) : where f' <0 and increasing at (0, ∞) where f' >0 . Therefore, the possible graph of the derivative of above graph is shown below.

The graph of f' have roots at x = 0 and x = 2 . The graph off should "bounce" off the x

axis at x = 2

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Most popular questions from this chapter

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.

$f (x) = 2 x^{3} - 9 x^{2} + 1$

For the graph of f in the given figure, approximate all the values x ∈ (0, 4) for which the derivative of f is zero or does not exist. Indicate whether f has a local maximum, minimum, or neither at each of these critical points.

Use the second-derivative test to determine the local extrema of each function $f$ in Exercises $29 - 40$ . If the second-derivative test fails, you may use the first-derivative test. Then verify your algebraic answers with graphs from a calculator or graphing utility. (Note: These are the same functions that you examined with the first-derivative test in Exercises $39 - 50$ of Section $3.2$ .)

$f (x) = (x - 2)^{2} (1 + x)$

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.

$f (x) = x^{2} (x - 1) (x + 1)$

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.

$f (x) = \frac{1}{{(x - 1)}^{2} (x - 2)}$

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Find the possibility graph of its derivative f'.

Short Answer

Step by step solution

Step 1. Given

Step 2. Explanation

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Most popular questions from this chapter

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