Question

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

Answer 1

If function is attaining maximum at $x=1$, then $f^{{}^{\prime }}\left(1\right)=0$.

Here $f^{{}^{\prime }}\left(x\right)=4x^3-124x+a$

$f^{{}^{\prime }}\left(1\right)=4-124+a$.
Putting this to zero,we get
$4-124+a=0$.

$\therefore a=120$