QJEEM06Mad3c1: JEE Main 2006 Mathematics - Class 12 JEEM06Mad3c1 Solution: The function f ( x ) = x 2 + 2 x has a local minimum at

Question

Verified Solution • 2025–26 Session moderate

The function

f (x) = \frac{x}{2} + \frac{2}{x}

has a local minimum at

Accepted Answer

f (x) = \frac{x}{2} + \frac{2}{x} \Rightarrow f^{'} (x) = \frac{1}{2} - \frac{2}{x^{2}} = 0

\Rightarrow x^{2} = 4

or

x = 2, - 2;

f^{″} (x) = \frac{4}{x^{3}}

f^{″} {(x)]}_{x = 2} = + v e \Rightarrow f (x)

has local min at

x = 2.

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