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Question

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


Solution

If function is attaining maximum at $$x=1$$, then $${f}^{'}(1)=0$$.
Here $${f}^{'}(x)=4{x}^{3}-124x+a$$
$${f}^{'}(1)=4-124+a$$.
Putting this to zero,we get 

$$4-124+a=0$$.
$$\therefore a=120$$

Mathematics

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