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 theo

Question

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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Kinsley 2 weeks 2021-10-11T00:10:15+00:00 1 Answer 0

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    2021-10-11T00:11:18+00:00

    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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