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Application of Derivatives question

2008 · Shift 0 · Q40

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PYQ Library
JEE Main
Mathematics
Application of Derivatives
2008 · Shift 0 · Q40

Application of Derivatives question

2008 · Shift 0 · Q40

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

Suppose the cubic

{x^3} - px + q

has three distinct real roots where

p\gt 0

and

q\gt 0

. Then which one of the following holds?

A
The cubic has minima at $\sqrt {{p \over 3}}$ and maxima at $-\sqrt {{p \over 3}}$
B
The cubic has minima at $-\sqrt {{p \over 3}}$ and maxima at $\sqrt {{p \over 3}}$
C
The cubic has minima at both $\sqrt {{p \over 3}}$ and $-\sqrt {{p \over 3}}$
D
The cubic has maxima at both $\sqrt {{p \over 3}}$ and $-\sqrt {{p \over 3}}$

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