Exercises

1. For each of the following functions, verify graphically that the MVT holds and find all values of c, a < c <b, that satisfy the condition

   

   1. , , b= 2.
   2. , a=2, b=5.
   3. , , .
   4. , a=-2, b=4.
2. Explain how the MVT applies to support the patrolman's claim.

3. For which values of a and b would the MVT apply to ?

4. Note that the derivative is not required to be continuous in the MVT. Can you come up with a function that is differentiable, but whose derivative is not continuous? ( Hint - if is differentiable on an interval , then the derivative cannot have any jump discontinuities. What other kinds of discontinuities are there?)