What do you mean "does not have a derivative at the point"? Do you mean undefined, constant, zero?

In terms of f'(x), a point of inflection occurs where f'(x) has a max/min, like you said. To solve for this you take the derivative of f'(x), which is f''(x) and set it equal to zero. So if you are looking at the f''(x) graph then you need to be looking for when f''(a)=0.