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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