The function f x = x 3 - a x has a local minimum at x = k , where k ≥ 2, then a possible value of a is

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The function

f (x) = x^{3} - a x

has a local minimum at

x = k,

where

k \geq 2,

then a possible value of

a

is

MathematicsApplication of DerivativesJEE Main

Options:

A $9$
B $11$
C $13$
D $8$

Solution:

1437 Upvotes Verified Answer

The correct answer is:

13

f^{'} (x) = 3 x^{2} - a = 0 \Rightarrow x = \pm \sqrt{\frac{a}{3}}

∴

f (x)

has local minimum at

x = + \sqrt{\frac{a}{3}} \Rightarrow \sqrt{\frac{a}{3}} \geq 2

\Rightarrow a \geq 12

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