When does a point of inflection occurs?

Question

When the value of the slope of the tangent to a function is (locally) at a maximum or minimum value, a point of inflection occurs. is that true or false?

Answer 1

True, this is because if f'(x) is at a local minimum or local maximum then f''(x) = 0. Also this means that f''(x) is going from positive to negative or negative to positive which indicates that a point of inflection has occurred.