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Local Maxima

If the functi...

Question

If the function $f (x) = x^{2} + a / x$ has a local minimum at x $= 2$ , then the value of a is

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none of these

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Solution

The correct option is B 16
Given, $f (x) = x^{2} + a / x$
$f^{'} (x) = 2 x - a / x^{2}$
Given $x = 2$ is local minima of $f (x)$
$f^{'} (2) = 0 = 4 - a / 4$
$\Rightarrow a = 16$

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