Verify that the function satisfies the three hypotheses of Rolle's theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's theorem. (Enter your answers as a comma- separated list.) f(x) = 3x2 - 6x + 8, (-1, 3] C =

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A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

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A: We have to evaluate the above integral.

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A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

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A: We need to integrate∫excos7excos4exdxSubstitute ex=tDifferentiate x w.r.t texdx=dtThen∫cos7tcos4tdt

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A: I am attaching image so that you understand each and every step.

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A: We need to choose correct option.