Notes - 4.2 - Rolle's and Mean Value Theorem

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  • 7/30/2019 Notes - 4.2 - Rolle's and Mean Value Theorem

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    Drill

    Look at the following graph. Notice that it is:

    1. continuous on [-2, 2]2. differentiable on (-2, 2)

    3. and f(2) = f(-2)

    Find the value of c, for which f (c) = 0

    1. Draw two more graphs that have the same three properties as above, including at least one place wheref (c) = 0, but which look different.

    2. Try to draw a graph that has the same three properties as above, but does NOT have a value c where f (c) =

    0

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    Notes 4.2

    First we have to talk another theorem

    ROLLES THEOREM

    _________________________ has three stipulations:

    1. f is ______________________________________________________________________

    2. f is ______________________________________________________________________

    3. _________________________________________________________________________

    If f satisfies the above three properties, then there is a numberc in (a, b) such that

    ____________________________________________________________________________

    MEAN VALUE THEOREM:

    _________________________ has two stipulations:

    1. f is _____________________________________________________________________________

    2. f is _____________________________________________________________________________

    If f satisfies the above three properties, then there is a numberc in (a, b) such that

    ___________________________________________________________________________________

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    GRAPHICAL EXPLANATION:

    EX 1: Verify that the function below satisfies the MVT, then find all numbers c that satisfy the conclusion ofthe MVT: f(x) = x3 on [-2, 2]

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