7. Let f be analytic in a domain D. Suppose that |f(z)| is constant on D, i.e., there is some c ER20 such that Vz Є D, |f(z)| = c. Prove that f(z) must be constant on D. Hint: It may be helpful to consider F.

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?