Differentiation

Please explain whether each statement is true or false.  Please give short explanation why and if false, please give an example.

The maximum of a function that is continuous on a closed interval can occur at two different values in the interval.

IF a function is continious on a closed interval, then it must have a minimum on the interval.

If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x) + k where k is a constant

If x = c is a critical number of the function f, then it is also a critical number of the function g(x) = f(x-k), where k is a constant.