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Question

It is given that at x=1, the function x462x2+ax+9 attains its maximum value, on the interval [0,2]. Find the value of a.

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Solution

If function is attaining maximum at x=1, then f(1)=0.
Here f(x)=4x3124x+a
f(1)=4124+a.
Putting this to zero,we get

4124+a=0.
a=120

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