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January 7th, 2017, 07:59 AM   #1
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Verifying 3 Hypotheses of Rolle's Theorem

Need help on this problem-

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.

f(x) = cos2x, [pi/8, 7pi/8]
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January 7th, 2017, 08:16 AM   #2
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start by stating the three hypotheses of Rolle's Theorem (a special case of the MVT) ...
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January 7th, 2017, 01:37 PM   #3
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Okay, what are those "three hypotheses"? What, precisely, does "Rolle's theorem say?
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January 13th, 2017, 11:51 PM   #4
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This is the Mean Value Theorem analytic proof, it will help you figure out 3 hypothesis of the Rolles Theorem, since the Mean Value Theorem is connected to the Rolles Theorem

https://mymathware.blogspot.nl/2017/...proof.html?m=1
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January 13th, 2017, 11:53 PM   #5
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Rolle's theorem essentially states that any real-valued differentiable function that attains equal values at two distinct points must have a stationary or critical point somewhere between them—that is, a point where the first derivative (the slope of the tangent line) is equal to zero.

https://mymathware.blogspot.nl/2017/...eorem.html?m=1
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January 14th, 2017, 04:42 AM   #6
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So, again, what are the "three hypotheses"?
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