   Chapter 4.1, Problem 12E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) Sketch the graph of a function on [−1, 2] that has an absolute maximum but no local maximum.(b) Sketch the graph of a function on [−1, 2] that has a local maximum but no absolute maximum.

(a)

To determine

To sketch: The graph of a function on [1,2] that has an absolute maximum but no local maximum.

Explanation

Let x be represented in the x-axis and the value of the function f(x) be represented in the y-axis.

Absolute maximum is any point of the domain at which the function attains its maximum value. Since the given interval is [1,2] , choose the maximum point at x = 2.

Local maximum is the point in the considered interval of the domain at which the function attains its maximum value

(b)

To determine

To sketch: The graph of a function on [1,2] and it satisfies the conditions that the graph has local maximum but no absolute maximum.

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