If f : [0, 3] → R is continuous, must its range be a closed interval?

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

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.

What does it mean to say that f(4) is a local maximum valueof f ?