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 October 21st, 2013, 05:46 AM #1 Senior Member   Joined: Apr 2013 From: Ramallah, Palestine Posts: 349 Thanks: 0 Help with Rolle's Theorem [2] Verify that the function satisfies the three hypothesis of Rolle's Theorem on the given interval. Then find all the numbers c that satisfy the conclusion of Rolle's Theorem. $f(x) = \sqrt{x} - \frac{1}{3}x f'(x) = \frac{1}{2}x^{-1/2} - \frac{1}{3} \frac{1}{2}x^{-1/2} - \frac{1}{3} = 0 \frac{1}{2}x^{-1/2} = \frac{1}{3} c = \frac{1}{9} / \frac{1}{4} = \frac{1}{9} * \frac{4}{1} = \frac{4}{9}$ $c= \frac{4}{9}$ so how are they getting $c= \frac{9}{4}$ ??
 October 21st, 2013, 06:05 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Help with Rolle's Theorem [2] What is the given interval?
 October 21st, 2013, 07:30 AM #3 Senior Member   Joined: Apr 2013 From: Ramallah, Palestine Posts: 349 Thanks: 0 Re: Help with Rolle's Theorem [2] [0,9]
 October 21st, 2013, 08:22 AM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Help with Rolle's Theorem [2] $\frac{1}{2\sqrt{x}}\,-\,\frac13\,=\,0 \\ \frac{1}{2\sqrt{x}}\,=\,\frac13 \\ \sqrt{x}\,=\,\frac32 \\ x\,=\,\frac94$
October 21st, 2013, 04:18 PM   #5
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Re: Help with Rolle's Theorem [2]

Quote:
 Originally Posted by Shamieh Verify that the function satisfies the three hypothesis of Rolle's Theorem on the given interval. Then find all the numbers c that satisfy the conclusion of Rolle's Theorem. $f(x) = \sqrt{x} - \frac{1}{3}x f'(x) = \frac{1}{2}x^{-1/2} - \frac{1}{3} \frac{1}{2}x^{-1/2} - \frac{1}{3} = 0 \frac{1}{2}x^{-1/2} = \frac{1}{3}$
The next line doesn't follow at all from the previous line. "x" has disappeared and "c" appeared. there is a "1/9" where before you had "1/3", etc.
Exactly what happened?

Quote:
 $c= \frac{1}{9} / \frac{1}{4} = \frac{1}{9} * \frac{4}{1} = \frac{4}{9}$ $c= \frac{4}{9}$ so how are they getting $c= \frac{9}{4}$ ??
(Yes, I know what you tried to do. Do it slowly, one step at a time, thinking about what you are doing on each step, and you should be able to see your error.

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