If the local minimum of the function f x = x 3 - 3 a 2 x + 4 ∀ a > 0 occurs at x = λ ∀ λ > 1 , then a may take the value

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Question: Answered & Verified by Expert

If the local minimum of the function

f (x) = x^{3} - 3 a^{2} x + 4 (\forall a > 0)

occurs at

x = λ (\forall λ > 1)

, then

a

may take the value

MathematicsApplication of DerivativesJEE Main

Options:

A $\frac{\sqrt{3}}{2}$
B $\frac{2}{\sqrt{3}}$
C $\frac{4}{5}$
D $0$

Solution:

1779 Upvotes Verified Answer

The correct answer is:

\frac{2}{\sqrt{3}}

f^{'} (x) = 3 x^{2} - 3 a^{2}

= 3 (x - a) (x + a)

Hence, minimum occurs at

x = a

∴ a > 1

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