Explanation Definition used. Concave up and Concave down Let f ( x ) be a curve with slope d y d x and second derivative f ″ ( x ) , then the curve is said to be concave up when f ″ ( x ) > 0 and the curve is said to be concave down when f ″ ( x ) < 0 . Further a curve is concave down at a maximum point and concave up at a minimum point. Inflection point The points at which the curve changes from concave up to concave down or concave down to concave up is called an inflection point. Calculation: Obtain the first derivative and critical values as follows. y ′ = 0 + 27 − 3 x 2 27 − 3 x 2 = 0 [ put y ′ = 0 for critical values ] 3 x 2 = 27 x 2 = 9 x = ± 3 Use the critical value x = − 3 , 3 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 = − 4 for interval x < − 3 . y ′ = 27 − 3 ( − 4 ) 2 = 27 − 3 ( 16 ) = 27 − 48 = − 21 < 0 Test the value x = − 1 for interval − 3 < x < 3 . y ′ = 27 − 3 x 2 = 27 − 3 ( − 1 ) 2 = 27 − 3 = 24 > 0 Test the value x = 4 for the interval x > 3 . y ′ = 27 − 3 ( 4 ) 2 = 27 − 3 ( 16 ) = 27 − 48 = − 21 < 0 Thus, the function is decreasing for x < − 3 and x > 3 and increasing for − 3 < x < 3

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 24.5, Problem 18E

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Sketch the graph with information and points from the first and second derivative of the function y=2+27x−x3 and verify the graph using a calculator.

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Chapter 24.5, Problem 17E

Chapter 24.5, Problem 19E

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Chapter 24 Solutions

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Ch. 24.1 - For the parabola y = 4 − x2, at the point (3, −5)...Ch. 24.1 - Prob. 2PE Ch. 24.1 - Prob. 1E Ch. 24.1 - Prob. 2E Ch. 24.1 - Prob. 3E Ch. 24.1 - Prob. 4E Ch. 24.1 - Prob. 5E Ch. 24.1 - Prob. 6E Ch. 24.1 - Prob. 7E Ch. 24.1 - Prob. 8E

Ch. 24.1 - Prob. 9E Ch. 24.1 - Prob. 10E Ch. 24.1 - Prob. 11E Ch. 24.1 - Prob. 12E Ch. 24.1 - In Exercises 11–14, find the equations of the...Ch. 24.1 - Prob. 14E Ch. 24.1 - Prob. 15E Ch. 24.1 - Prob. 16E Ch. 24.1 - Prob. 17E Ch. 24.1 - Prob. 18E Ch. 24.1 - Prob. 19E Ch. 24.1 - Prob. 20E Ch. 24.1 - Prob. 21E Ch. 24.1 - Where does the normal line to the parabola y = x —...Ch. 24.1 - Prob. 23E Ch. 24.1 - Prob. 24E Ch. 24.1 - A certain suspension cable with supports on the...Ch. 24.1 - Prob. 26E Ch. 24.1 - Prob. 27E Ch. 24.1 - Prob. 28E Ch. 24.1 - Prob. 29E Ch. 24.1 - Prob. 30E Ch. 24.2 - In Example 1, let x1 = 0.3, and find x2. 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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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Sketch the graph with information and points from the first and second derivative of the function y = 2 + 27 x − x 3 and verify the graph using a calculator.

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Sketch the graph with information and points from the first and second derivative of the function y=2+27x−x3 and verify the graph using a calculator.

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Chapter 24 Solutions