# 11. 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.

$f(x) =x ^4 - 62x^2 + ax + 9$
Function $f(x) =x ^4 - 62x^2 + ax + 9$ attains maximum value at x = 1 then x must one of the critical point of the given function that means
$f^{'}(1)=0$
$f^{'}(x) = 4x^3-124x+a\\ f^{'}(1) = 4(1)^3-124(1)+a\\ f^{'}(1)=4-124+a = a - 120\\$
$f^{'}(1)=0\\ a - 120=0\\ a=120$