a differentiable function y =f(x) that has the given properties.

Question

1. local minimum at (1,1), and local maximum at (3,3)

2. local minima at (1,1) and (3,3)

3. local maxima at (1,1) and (3,3)

I don't remember how to do this. Thank you.

http://en.wikipedia.org/wiki/Maxima_and_minima

I don't see how any function can have a local minima and maxima at the same point.

That is 3 different problems.