It is given that at x = 1, the function x^4 - 62x^2 + ax + 9 atta… - Vidyadip

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.

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Answer

Let $\text{f}\text{(x)}=\text{x}^4-62\text{x}^2+a\text{x}+9$ $\Rightarrow\ \text{f}'\text{(x)}=4\text{x}^3-124\text{x}+\text{a}$
Since, f(x) attains its maximum value at x = 1 in the interval [0, 2], therefore f'(1) = 0
$\therefore\ \text{f}'(1)=4-124+\text{a}=0$ $\Rightarrow\ \text{a}-120=0\ \Rightarrow\ \text{a}=120$

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