Section 4.2 Read Rolle's Theorem and the Mean Value Theorem carefully.  Scan the proofs.  Pay close attention to Figures 3 and 4 and be sure to notice Theorems 5 and 7.  Theorem 7 is not a big deal right now, but it will be later.  Answer the following questions by 7:00 am.  Send an e-mail with subject line MA251 to selliott@utm.edu .

1) Fill in the blanks:  The mean value theorem requires that f be a ______ function defined on a _______ interval .  f must also be ________ on an ______ interval

Continuous, closed; differentiable, open
Jacob Buttrey


2) Finish the sentence:  The main significance of the MVT is that it enables us to . . .

Obtain information about a function from information about it's derivative
Archie Rich


3) Fill in the blank:  If f '(x) = 0 for all x in an interval (a,b), then f is _______ on (a,b)
.

  1. constant
Matthew Thomas