If the function f ( x ) = x 4 - 62 x 2 + a x + 9 attains its local maximum value at x = 1 , then a is equal to:

Question

If the function $f (x) = x^{4} - 62 x^{2} + a x + 9$ attains its local maximum value at $x = 1$ , then $a$ is equal to:

Smart Achievers · Accepted Answer

(1)

Ans. 120

Explanation:

Here, $f (x) = x^{4} - 62 x^{2} + a x + 9$

$\frac{d f (x)}{d x} = \frac{d (x^{4} - 62 x^{2} + a x + 9)}{d x} = 4 x^{3} - 124 x + a$

$4 x^{3} - 124 x + a = 0$

Putting $x = 1$ , at which attains local maxima,

$4 - 124 + a = 0$

$a = 120$

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