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January 7th, 2017, 07:59 AM  #1 
Newbie Joined: Jan 2017 From: Texas Posts: 1 Thanks: 0  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] 
January 7th, 2017, 08:16 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,097 Thanks: 972 
start by stating the three hypotheses of Rolle's Theorem (a special case of the MVT) ...

January 7th, 2017, 01:37 PM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,210 Thanks: 555 
Okay, what are those "three hypotheses"? What, precisely, does "Rolle's theorem say?

January 13th, 2017, 11:51 PM  #4 
Newbie Joined: Jan 2017 From: Nigeria Posts: 5 Thanks: 0 Math Focus: Real Analysis and Fluid Mechanics 
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 
January 13th, 2017, 11:53 PM  #5 
Newbie Joined: Jan 2017 From: Nigeria Posts: 5 Thanks: 0 Math Focus: Real Analysis and Fluid Mechanics 
Rolle's theorem essentially states that any realvalued differentiable function that attains equal values at two distinct points must have a stationary or critical point somewhere between themâ€”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 
January 14th, 2017, 04:42 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,210 Thanks: 555 
So, again, what are the "three hypotheses"?


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hypotheses, rolle, theorem, verifying 
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