Suppose the cubic `x^(3)-px+q` has three distinct real roots, where `pgt0` and `qgt0`. Then which one of the following holds?

Options

A. The cubic has minima at `sqrt((p)/(3))` and maxima at `- sqrt((p)/(3))`
B. The cubic has minima at `- sqrt((p)/(3))` and maxima at `sqrt((p)/(3))`
C. The cubic has minima at both `sqrt((p)/(3))` and `-sqrt((p)/(3))`
D. The cubic has maxima at both `sqrt((p)/(3)) and - sqrt((p)/(3))`

Answer

A