Question:
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 $a$.
Solution:
Let $f(x)=x^{4}-62 x^{2}+a x+9$
$\therefore f^{\prime}(x)=4 x^{3}-124 x+a$
It is given that function f attains its maximum value on the interval [0, 2] at x = 1.
$\therefore f^{\prime}(1)=0$
$\Rightarrow 4-124+a=0$
$\Rightarrow a=120$
Hence, the value of a is 120.
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