Maxima and MinimaHard
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?
Options
A.The cubic has minima at 
and maxima at 
and maxima at B.The cubic has minima at and maxima at
and maxima at C.The cubic has minima at both 
and
and D.The cubic has maxima at both and
and Solution
Let f(x) = x3 - px + q
Now for maxima/minima
f′(x) = 0
⇒ 3x2 - p = 0
⇒ x2 =
∴ x = ±
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