Explanation The given equation of the function is y = 20 + 16 x − 4 x 2 . Calculate the first derivative as shown below. y = 20 + 16 x − 4 x 2 y ′ = 0 + 16 − 8 x Equate the first derivative to zero and obtain the critical values as shown below. 16 − 8 x = 0 8 x = 16 x = 2 Use the critical value x = 2 to subdivide the x -axis into subintervals. Select a test value within each test interval to determine the sign of derivative. Test the value x = 1 for interval x < 2 . y ′ = 16 − 8 ( 1 ) = 16 − 8 = 8 > 0 Test the value x = 3 for interval x > 3 . y ′ = 16 − 8 ( 3 ) = 16 − 24 = − 8 < 0 Thus, the function is decreasing for x > 2 and increasing for x < 2 . Substitute the critical values in the given function, to obtain the local minimum and local maximum

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Chapter 24.5, Problem 22E

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To sketch: The graph of the function y=20+16x−4x2 along with points from the first and second derivative.

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Chapter 24.5, Problem 21E

Chapter 24.5, Problem 23E

Chapter 24 Solutions

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Prob. 48RE Ch. 24 - Prob. 49RE Ch. 24 - Prob. 50RE Ch. 24 - Prob. 51RE Ch. 24 - Prob. 52RE Ch. 24 - In Exercises 49–94, solve the given problems. 53....Ch. 24 - Prob. 54RE Ch. 24 - Prob. 55RE Ch. 24 - Prob. 56RE Ch. 24 - The deflection y (in m) of a beam at a horizontal...Ch. 24 - Prob. 58RE Ch. 24 - Prob. 59RE Ch. 24 - Prob. 60RE Ch. 24 - Prob. 61RE Ch. 24 - Prob. 62RE Ch. 24 - In Fig. 24.75, the tension T supports the 40.0-N...Ch. 24 - Prob. 64RE Ch. 24 - Prob. 65RE Ch. 24 - Prob. 66RE Ch. 24 - An analysis of the power output P (in kW/m3) of a...Ch. 24 - The altitude h (in ft) of a certain rocket as a...Ch. 24 - Prob. 69RE Ch. 24 - Prob. 70RE Ch. 24 - Prob. 71RE Ch. 24 - Prob. 72RE Ch. 24 - Prob. 73RE Ch. 24 - A special insulation strip is to be sealed...Ch. 24 - Prob. 75RE Ch. 24 - Prob. 76RE Ch. 24 - Prob. 77RE Ch. 24 - Prob. 78RE Ch. 24 - Prob. 79RE Ch. 24 - Prob. 80RE Ch. 24 - Prob. 81RE Ch. 24 - Prob. 82RE Ch. 24 - Prob. 83RE Ch. 24 - Prob. 84RE Ch. 24 - Prob. 85RE Ch. 24 - Prob. 86RE Ch. 24 - 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Sine, Cosine and Tangent graphs explained + how to sketch | Math Hacks; Author: Math Hacks;https://www.youtube.com/watch?v=z9mqGopdUQk;License: Standard YouTube License, CC-BY

The graph of the function y = 20 + 16 x − 4 x 2 along with points from the first and second derivative.

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To sketch: The graph of the function y=20+16x−4x2 along with points from the first and second derivative.

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Chapter 24 Solutions