Question: Consider the general cubic polynomial f(x) = x 3 + ax 2 + bx + c, where a, b, and c are real numbers. a.

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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