# finding minimum and maximum of a function at given intervals

here is the question:

(-1, 7/2)

My working:

I know that by plugging in 0 into the equation you get -1 but I don't understand how to get 7/2

thank you

Hint: $f(x) = -2(x-\frac32)^2 + \frac72$. So the maximum is when the quadratic term is zero.
You don't need derivatives at all. The only candidates for min and max are clearly $0$, $2$ and $3/2$.