Yep, f'(r) = 0 if and only if r= 3B/2A
Then for c you need to find f''(r) and when you test the critical point in the second derivative: if f''(r) > 0 the it's a Local min. or if f''(r) < 0 then it's a local max.
For positive constants A and B, the force between two atoms in a molecule is given by the following equation, where r > 0 is the distance between the atoms.
f(r)=-(A/r^2)+(B/r^3)
(a) Find f '(r)
(b) Find the critical point for f(r).
(c) Classify the critical point as a minimum, maximum, or neither.
(d) Find the inflection point for f(r).
I found f'(r) and I got the critical point to be (3b/2a), but am not so sure about that.
Thanks in advance,
Tyler