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October 5th, 2012, 07:20 PM   #1
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Rolle's Theorem

y = f(x) = (x-3) (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
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October 5th, 2012, 08:55 PM   #2
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Re: Rolle's Theorem

Rolle's theorem states:

Let be a function that is continuous on and differentiable on . If , then there exists a number in such that .

, 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 end-point of the interval, and we find:

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October 6th, 2012, 07:17 AM   #3
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Re: Rolle's Theorem

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