Explanation f ( x ) = x ( 10 − x ) , [ − 1 , 3 ] f ( x ) = x ( 10 − x ) = 10 x − x 2 Then f ' ( x ) = 10 − 2 x So that x = 5 is the only critical point As this critical point is not in the interval [ − 1 , 3 ] We only need to check the value of f at the endpoint to determine the extreme value, Because f ( − 1 ) = − 11</

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Chapter 4, Problem 29CRE

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f(x)=x(10−x),[−1,3]

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Chapter 4, Problem 28CRE

Chapter 4, Problem 30CRE

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Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ 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 Ch. 4.1 - Prob. 6E

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f ( x ) = x ( 10 − x ) , [ − 1 , 3 ]

Solution Summary: The author explains that if f(x)=x(10-x), while the minimum value is -11, we can determine the extreme value.

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f(x)=x(10−x),[−1,3]

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Chapter 4 Solutions