Fine the absolute minimum and absolute maximum of the function on the interval [0,6]

I did the minimum already, it's just the maximum.

f(x) = x

f'(x) = 1

g'(x) = 2x

Bottom is never 0, so do the quadratic formula on the top:

Which in the end gave me 4 and -4, which when plugging into F(x) gave me and

But plugging 6 in gave me

Is this valid?