here is the question:
here is the correct answer:
I know that by plugging in 0 into the equation you get -1 but I don't understand how to get 7/2
Hint: $f(x) = -2(x-\frac32)^2 + \frac72$. So the maximum is when the quadratic term is zero.
Apply the second derivative test to get minima/maxima of the function. Don't forget to check the boundaries of the interval.
You don't need derivatives at all. The only candidates for min and max are clearly $0$, $2$ and $3/2$.