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  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?)

Sean O Anderson
Wed Sep 27 09:31:40 EDT 1995