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

1 Answer
Jul 6, 2016

Critical points r_j make the derivative D'(r_j)=0. We them have to determine whether they are maxima, minima or inflexion.

Explanation:

The first derivative is D'(r)= -2r-2, so we find the critical points by solving -2r-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.

Please observe that this is coherent, as the graph is a parabola pointing downwards, so it has a single maximum