1. Why is a stationary point often called a local maximum point?
The reason is that there is often higher y-values of the function at other places on the graph. i.e On a cubic with a positive cubed term the function increases indefinitely as x increases.
2. Can a point of inflection also be a stationary point?
Yes, for example, the function y = x3 has a stationary point of inflection at (0, 0)
3. Can a function have more than one stationary point?
Yes, for example, most cubic functions have both a local maximum point and a local minimum point.
4. What is an example of a function where when f '(x) = 0 then f ''(x) = 0?
f(x) = x5 is such an example. This has a increasing point of inflection at x = 0