## Exercises - Applications of MVT

We start with problems solved using the fact that a function whose
derivative is zero inside an interval must be constant on this interval,
there are three variations on this topic here.
The next batch of problems proves
inequalities by direct application of MVT
and using derivative.
At the end there are problems on
root counting

Monotonicity and derivative can be also used to prove that a function is 1-1.
For problems of this kind see
1-1 and inverse functions
in Functions - Exercises.

If you want to refer to sections of Methods Survey while working the exercises,
you can click
here and it will appear in a
separate full-size window. Similarly,
here we offer Theory.

Prove that the following equalities are true on indicated sets.

For each of the following equalitites, find the set on which it is true.

For each of the following functions prove that there is a set *M* and a
constant *k* such that the function is equal to *k* on *M*.

Prove the following inequalities on given sets.

For each of the following function determine the number of its roots. Then
identify positions of these roots by placing each within two successive
integers.

Back to Exercises