Explanation Given information: The given function is f ( x ) = 3 x 4 − 2 x 3 + 4 . Formula used: The formula to calculate the differential of a function h ( x ) = [ g ( x ) ] n by General Power Rule is, h ′ ( x ) = n [ g ( x ) ] n − 1 ⋅ g ′ ( x ) Calculation: The given function is, f ( x ) = 3 x 4 − 2 x 3 + 4 (1) Differentiate equation (1) with respect to x on both sides to evaluate f ′ ( x ) . f ′ ( x ) = 3 ⋅ 4 x 3 − 2 ⋅ 3 x 2 + 0 [ Use General Power Rule d d x ( x n ) = n x n − 1 , n > 0 ] = 12 x 3 − 6 x 2 = 6 x 2 ( 2 x − 1 ) Substitute 0 for f ′ ( x ) in above equation. 0 = 6 x 2 ( 2 x − 1 ) Equate each factor equal to 0 to find the value of x . 6 x 2 = 0 x = 0 Now equate 2 x − 1 to 0 and find the value of x . 2 x − 1 = 0 2 x = 1 x = 1 2 The critical numbers for the function f are 0 , 1 2

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Author: Tan

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Chapter 4.1, Problem 66E

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To find: The relative maxima and relative minima of given function.

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Chapter 4.1, Problem 65E

Chapter 4.1, Problem 67E

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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 relative maxima and relative minima of given function.

Solution Summary: The author explains the relative maxima and relative minima of a given function.

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