Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

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

The possible graph of f is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The given sign chart is

Step 2. Sketch the graph of f.

To sketch the possible graph of f, we will use theorem 3.6 and 3.10.

Theorem 3.6 states that the Derivative Measures Where a Function is Increasing or Decreasing, let f be a function that is differentiable on an interval I.

(a) If $f'$ is positive in the interior of I, then f is increasing on I.

(b) If $f'$ is negative in the interior of I, then f is decreasing on I.

Theorem 3.10 states that the Second Derivative Determines Concavity, suppose both f and $f'$ are differentiable on an interval I.

(a) If $f''$ is positive on I, then f is concave up on I.

(b) If $f''$ is negative on I, then f is concave down on I.

Step 3. The graph of f.

From the given chart, we conclude that

$f'$ is positive on the intervals $(- \infty, 0) a n d (2, \infty)$ and negative on the intervals $(0, 1) a n d (1, 2) .$ Thus, f will we increase on the positve intervals and decrease on the negative intervals.

$f''$ is positive on the interval $(1, \infty)$ and negative on the interval $(- \infty, 1) .$ Thus, f will be concave up on the positive intervals and concave down on the negative intervals.

The graph is

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Calculus

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Short Answer

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

Step by Step Solution

Step 1. Given Information.

Step 2. Sketch the graph of f.

Step 3. The graph of f.

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Calculus

Answers without the blur.

Short Answer

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

Step by Step Solution

Step 1. Given Information.

Step 2. Sketch the graph of f.

Step 3. The graph of f.

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