Explanation Definition used: Critical point: A point whose x- coordinate is the critical number c such that either f ′ ( c ) = 0 or f ′ ( c ) does not exists and y -coordinate is f ( c ) . Increasing function: Let f be a function with some derivative defined on some interval. Then the function is said to be increasing if for any x in the interval, the inequality f ′ ( x ) > 0 holds. Decreasing function: Let f be a function with some derivative defined on some interval. Then the function is said to be decreasing if for any x in the interval, the inequality f ′ ( x ) < 0 holds. Calculation: The given function is f ( x ) = 4 x 3 + 8 x 2 − 16 x + 11 . Obtain the derivative as follows. f ′ ( x ) = 4 ( 3 x 2 ) + 8 ( 2 x ) − 16 ( 1 ) + 0 = 12 x 2 + 16 x − 16 Set y ′ ( c ) = 0 and compute the value of c . 12 c 2 + 16 c − 16 = 0 3 c 2 + 4 c − 4 = 0 3 c 2 + 6 c − 2 c − 4 = 0 3 c ( c + 2 ) − 2 ( c + 2 ) = 0 That is, 3 c ( c + 2 ) − 2 ( c + 2 ) = 0 ( 3 c − 2 ) ( c + 2 ) = 0 3 c − 2 = 0 or c + 2 = 0 c = 2 3 or c = − 2 Thus, the critical numbers is 2 3 and − 2 . These points determines the intervals, ( − ∞ , − 2 ) ∪ ( − 2 , 2 3 ) ∪ ( 2 3 , ∞ )

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Chapter 13, Problem 20RE

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To find: The open intervals where f(x)=4x3+8x2−16x+11 increases or decreases.

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Chapter 13, Problem 19RE

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Chapter 13 Solutions

EBK FINITE MATHEMATICS AND CALCULUS WIT

Ch. 13.1 - Find where the function is increasing and...Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 1WE Ch. 13.1 - Prob. 2WE Ch. 13.1 - Prob. 3WE Ch. 13.1 - Prob. 4WE Ch. 13.1 - Prob. 5WE Ch. 13.1 - Prob. 6WE

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The open intervals where f ( x ) = 4 x 3 + 8 x 2 − 16 x + 11 increases or decreases.

Solution Summary: The author explains that the function increases or decreases on the intervals (-infty,-2)and

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To find: The open intervals where f(x)=4x3+8x2−16x+11 increases or decreases.

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Chapter 13 Solutions