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).

- constant