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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

HOW DO YOU SEE IT? The graph of f is shown in the figure.

images

(a) For which values of x is f'(x) zero? Positive? Negative? What do these values mean?

(b) For which values of x is f"(x) zero? Positive? Negative? What do these values mean?

(c) On what open interval is f' an increasing function?

(d) For which value of x is f'(x) minimum? For this value of x, how does the rate of change of f compare with the rates of change of f for other values of x? Explain.

(a)

To determine

To calculate: The values over which the first derivative is 0, positive and negative for the provided graph

images

Explanation

Given:

The graph of the function f:

Formula used:

The function is said to be increasing for x(a,b) if f'(x)>0 and it is said to be decreasing for x(a,b) if f'(x)<0.

Also, the first derivative of the function is 0 at its critical points where the relative extremas may occur

(b)

To determine

To calculate: The values over which the second derivative is 0, positive and negative for the provided graph

images

(c)

To determine

To calculate: The interval on which the derivative of the function is increasing for the provided graph

images

(d)

To determine

To calculate: The value where the derivative is maximum for the provided graph

images

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