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17 May, 02:58

Determine whether Rolle's Theorem can be applied to the function on the given interval; if so, find the value (s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. If Rolle's Theorem does not apply, enter DNE.) f (x) = x (5 - x) on [0, 5]

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  1. 17 May, 05:28
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    Step-by-step explanation:

    1) Check if the function is differentiable on that interval. In this case, yes, because all polynomials are differentiable.

    2) plug in the bounds of the interval to see if the y-values equal 0.

    f (0) = 0

    f (5) = 0

    since the last 2 conditions are satisfied, DNE will not be an answer choice.

    3) take derivative and make it equal to 0

    f' (*) = 5 - 2x

    0 = 5 - 2x

    x = 5/2

    4) at c = 5/2, f (x) satisfies rolle's theorem.
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