Explanation Given information: The given function is, g ( x ) = − x 2 + 4 x + 3 (1) Theorem used: If f has a local maximum or local minimum value at c and f ′ ( c ) exists, then f ′ ( c ) = 0 . Calculation: Let the function is defined on the interval ( − ∞ , ∞ ) . First find the critical points on the graph of given function. Obtain the first derivative of the function g ( x ) = − x 2 + 4 x + 3 . g ′ ( x ) = d d x ( − x 2 + 4 x + 3 ) = d d x ( − x 2 ) + d d x ( 4 x ) + d d x ( 3 ) = − 2 x + 4 + 0 = − 2 x + 4 Set the above derivative equal to zero and obtain the critical point. − 2 x + 4 = 0 − 2 x = − 4 x = − 4 2 x = 2 The critical point is x = 2

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ISBN: 9781305041264

Author: Tan

Publisher: CENGAGE C

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Chapter 4.4, Problem 10E

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The absolute maximum and minimum for the function g(x)=−x2+4x+3 .

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Chapter 4.4, Problem 9E

Chapter 4.4, Problem 11E

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Ch. 4.1 - Explain each of the following: a. f is increasing...Ch. 4.1 - Prob. 2CQ Ch. 4.1 - Prob. 3CQ Ch. 4.1 - Prob. 4CQ Ch. 4.1 - Prob. 5CQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E

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The absolute maximum and minimum for the function g ( x ) = − x 2 + 4 x + 3 .

Solution Summary: The author explains how to find the absolute maximum and minimum value for the function g(x).

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To find:

The absolute maximum and minimum for the function g(x)=−x2+4x+3 .

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Chapter 4 Solutions

The absolute maximum and minimum for the function g ( x ) = − x 2 + 4 x + 3 .

Solution Summary: The author explains how to find the absolute maximum and minimum value for the function g(x).

Concept explainers

Videos

To find: The absolute maximum and minimum for the function g(x)=−x2+4x+3 .

Want to see the full answer?

Chapter 4 Solutions

To find:

The absolute maximum and minimum for the function g(x)=−x2+4x+3 .