Suppose f: R R is continuous and periodic with period P > 0. That is, f (x + P) = f (x) for all x E R. Show that f achieves an absolute minimum and an absolute maximum.

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?