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

`f(x)=x^4-62x^2+ax+9`
`f'(x)=4x^3-124x+a`
at `x=1`, the function has maximum value `f'(1)=0 implies4(1)^2-124(1)+a=0, a=120`
when `a=120`, the function attains maximum value.