Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.
$f (x) = 3 x - 2 e^{x}$

The critical point is $x = I n (\frac{3}{2})$ . The graph of the given function is shown below .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information .

Consider the given function $f (x) = 3 x - 2 e^{x}$ .

Step 2. Find the critical points .

The critical points are the points where the function is defined and its derivative is zero or undefined .

Differentiate the given function .

$f (x) = 3 x - 2 e^{x} f' (x) = 3 - 2 e^{x}$

Therefore the critical point is $x = I n (\frac{3}{2})$ .

Step 3. Plot the graph .

The graph of the given function is shown below .

From the given graph the function f has local minimum because the turning point is on negative axis .

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Calculus

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Short Answer

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.
$f (x) = 3 x - 2 e^{x}$

Step by Step Solution

Step 1. Given information .

Step 2. Find the critical points .

Step 3. Plot the graph .

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Step by Step Solution

Step 1. Given information .

Step 2. Find the critical points .

Step 3. Plot the graph .

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Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.
$f (x) = 3 x - 2 e^{x}$