Suppose the cubic has three distinct real roots

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Suppose the cubic

x^3 - px + q = 0

has three distinct real roots, where

p > 0

and

q < 0

. Which one of the following holds? (1) The cubic has minima at

\left(-\sqrt{\frac{p}{3}}\right)

and maxima at

\sqrt{\frac{p}{3}}

(2) The cubic has minima at both

\sqrt{\frac{p}{3}}

and

-\sqrt{\frac{p}{3}}

(3) The cubic has maxima at both

\sqrt{\frac{p}{3}}

and

-\sqrt{\frac{p}{3}}

(4) The cubic has minima at

\sqrt{\frac{p}{3}}

and maxima at

-\sqrt{\frac{p}{3}}