Question
Suppose the cube x3– px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?
-
The cubic has minima at
and maxima at –
-
The cubic has minima at –
and maxima at
-
The cubic has minima at both
and- 
-
The cubic has maxima at both
and- 
Solution
A.
The cubic has minima at and maxima at –
Let f(x) = x3– px + q
Now for maxima/minima
f′(x) = 0
⇒ 3x2– p = 0
⇒ x2
= p/3
