Question

Properties of cubics: Consider the general cubic polynomial f(x)=x^3+ax^2+bx+c, where a,b, and c are real numbers.
a.Prove that f has exactly one local min. and one local max. provided that a^2>3b
b. Prove that f has no extreme values if a^2<3b.

Answer 1

You need to find the extrema by finding the derivative and then solving for x.