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