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Q.
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 $a$.
Application of Derivatives
Solution:
Let $f(x) = x^4 - 62x^2 + ax + 9$. Then,
$f(x) = 4x^3 - 124x + a$.
It is given that $f(x)$ attains its maximum at $x = 1$.
$\therefore f'\left( 1 \right) = 0$
$\Rightarrow 4 - 124 + a = 0$
$\Rightarrow a = 120$