# How do you find all critical point and determine the min, max and inflection given D(r)=-r^2-2r+8?

Critical points ${r}_{j}$ make the derivative $D ' \left({r}_{j}\right) = 0$. We them have to determine whether they are maxima, minima or inflexion.
The first derivative is $D ' \left(r\right) = - 2 r - 2$, so we find the critical points by solving $- 2 r - 2 = 0$, which only solution is $r = - 1$. We then calculate the second derivative in $r = - 1$; the second derivative is $D ' ' = - 2$, which is negative everywhere, so it is negative in the critical point $r = - 1$. The function therefore has a maximum at the point $r = - 1$.