Question
Mathematics Question on Applications of Derivatives
It is given that at x = 1, the function x4−62x2+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.
Answer
Let f(x) = x4−62x2+ax+9.
f'(x)=4x3-124x+a
It is given that function f attains its maximum value on the interval [0, 2] at x = 1.
f'(1)=0
=4-124+a=0
a=120
Hence, the value of a is 120.