For example on the graph f(x)= x^3, f'(x)= 3x^2. set it to 0 and u get x=0 does that qualify as a critical point since its not a max or a min, though it changes concavity. do inflection points classify as critical points?
Yes, critical points are points where the slope is either zero or undefined...but a stationary point is a type of critical point [point where derivative is 0]. So a statitionary point is a critical point, but not all critical points are stationary points...
Just a thought to throw out there.
--Chris