Given function: f(x)=x4−62x2+2ax+b
The function attains its maximum value at x=1 on the interval [0,2].
At a maximum point, the first derivative equals zero.
Taking the derivative of f(x)=x4−62x2+2ax+b:
f′(x)=4x3−124x+2a
Since the maximum occurs at x=1:
f′(1)=0
Substituting x=1:
4(1)3−124(1)+2a=0
4−124+2a=0
−120+2a=0
2a=120
a=60
Therefore, a=60