Explanation Given: The function is y = t 3 − 6 t 2 + 4 . Formula used: Test for concavity: Let f ″ ( x ) exist for all x ∈ ( a , b ) , then • y = f ″ ( x ) > 0 for all x ∈ ( a , b ) , here the function f is concave upward on ( a , b ) . • y = f ″ ( x ) < 0 for all x ∈ ( a , b ) , here the function f is concave downward on ( a , b ) . y = f ( x ) has a point of inflection if f ″ ( x ) = 0 . Calculation: The function is y = t 3 − 6 t 2 + 4 . Let f ( t ) = t 3 − 6 t 2 + 4 . … (1) First, find the derivative. f ′ ( t ) = 3 t 3 − 1 − 6 ( 2 ) t 2 − 1 = 3 t 2 − 12 t Now, find the second derivative

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Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.4, Problem 6E

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Write the intervals on which the function is concave up or down. Also, find the points of inflection.

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Chapter 4.4, Problem 5E

Chapter 4.4, Problem 7E

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Chapter 4 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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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Write the intervals on which the function is concave up or down. Also, find the points of inflection.

Solution Summary: The author explains how the function is concave up and down, and the points of inflection.

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Chapter 4 Solutions