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Q21E

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Essential Calculus: Early Transcendentals
Found in: Page 209
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Short Answer

Sketch the graph of \(f\) by hand and use your sketch to find the absolute and local maximum and minimum values of \(f\). (Use the graphs and transformations of Sections 1.2.)

21. \(f(x) = 1 - \sqrt x \)

The absolute maximum occurs at \(x = 0\). There is no absolute minimum as well as the local extrema.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given data

The given function is \(f(x) = 1 - \sqrt x \).

Step 2: Concept of Differentiation

Differentiation is a method of finding the derivative of a function. Differentiation is a process, where we find the instantaneous rate of change in function based on one of its variables.

Step 3: Sketch the graph of the function

Let \(y = f(x)\).

Obtain the values of \(y\) for various values of \(x\) as shown in below table and draw the graph of \(f(x)\) as shown below in Figure 1.

From Figure 1, it is observed that there is no absolute minimum and local extrema as the curve approaches numerically large values.

Notice that the only highest point of the curve occurs at \(x = 0\). Therefore, the absolute maximum value is \(f(0) = 1\).

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Explain the difference between an absolute minimum and a local minimum.

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(e) Use part (d) to write the volume as a function of one variable.

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