It is given that at `x=1` , the function `x^4-62 x^2+a x+9` attains its maximum value on the interval `[0,\ 2]` . Find the value of `a` .

Explanation

Let ` f(x) = x^(4) - 62x^(2) + ax + 9`
` f'(x) = 4x^(3) - 124x + a`
It is given that the maximum value of f in the interval [0, 2] is at x = 1.
f'(1) = 0
` rArr 4 xx 1^(3) - 124 xx 1+ a=0`
` rArr 4-124 + a = 0 rArr a = 120 ` .