October 5th, 2012, 07:20 PM  #1 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Rolle's Theorem
y = f(x) = (x3) (x+1)^(2) on [1,3] closed interval Can Rolle's Theorem be applied to this function on [1,3] I said Yes because I set each to zero and got zero for both therefore if f '(a) = f '(b) then f '(c) must exist please someone check to see if I did this properly Next it says if Rolle's Theorem can be applied, find all values, C, in the open interval (1,3) such that f ' (c) = 0 I need some help with this second question 
October 5th, 2012, 08:55 PM  #2  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Rolle's Theorem
Rolle's theorem states: Quote:
, and the function is continuous and differentiable for all reals (and so it is thus on the given interval) we know by Rolle's theorem there is at least one critical number on the given interval. To find the critical number(s), we equate the derivative to zero, and solve for . Using the product rule, we find: We discard the root as it is an endpoint of the interval, and we find:  
October 6th, 2012, 07:17 AM  #3 
Senior Member Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0  Re: Rolle's Theorem
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