Let ƒ : R → R be a continuous function satisfying ƒ(0) = 1. Show that there is a € > 0 such that f(x) 0.137 for all x = (-ε, e).

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 is the purpose of the Intermediate Value Theorem?