Consider the general cubic polynomial f(x) = x 3 + ax 2 + bx + c, where

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Consider the general cubic polynomial f(x) = x3 + ax2 + bx + c, where a, b, and c are real numbers.

a. Prove that f has exactly one local maximum and one local minimum provided that a2 > 3b.

b. Prove that f has no extreme values if a2 < 3b.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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