Question

Suppose the cubic x³ – px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

(a) The cubic has maxima at both √(p/3) and - √(p/3)

(b) The cubic has minima at √(p/3) and maxima at - √(p/3)

(c)  The cubic has minima at - √(p/3) and maxima at √(p/3)

(d) The cubic has minima at both √(p/3) and - √(p/3)

Answer 1

(b) : Denote x³ – px + q by f(x)
i.e. f(x) = x³ – px + q
Now for expression, f '(x) = 0, i.e. 3x² – p = 0