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^23b b. Prove that f has no extreme values if a^2

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.
c. Prove that for all real values of a,b,and c, the function has exactly one inflection point. Where is the inflection point located?

anonymous · Answer

I got the answer of C, but im confused about part a and b :(