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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Sketch the graph of a function f that is continuous on [1, 5] and has the given properties.

Absolute maximum at 5, absolute minimum at 2, local maximum at 3, local minima at 2 and 4

To determine

To sketch: The graph of a function f which is continuous on [1,5] and satisfying the conditions that the graph has absolute maximum at 5, absolute minimum at 2, local maximum at 3 and local minima at 2 and 4.

Explanation

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

Since the absolute maximum occurs at the point 5, choose the greatest point on the x-axis.

That is, mark the point on (5, 3).

Since the absolute minimum occurs at the point 2, choose the least integer value on y-axis.

That is, mark the point on (2, 1).

Since the local maximum occurs at the point 3, plot the point on (3, 2).

Since the local minima occur at 3 and 4, plot the point on (2, 1) and (4, 1).

Draw the graph of the function f in such a way that it satisfies the above conditions as shown below in Figure 1

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