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Determine whether Rolle's theorm can be applied on the closed interval [a, b]. If Rolle's theorm can be applied, find all vales of c in the interval [a,b] such that f'(c)=0. If Rolle's theorm cannot be applied, explain why not.

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f(x)=(x-1)(x-2)(x-3), [1,3]
since \[f(1)=f(3)=0\] and since any polynomial is differentiable you can use rolle
\[f(x)=x^3-6 x^2+11 x-6\] \[f'(x)=3x^2-12x+11\] so rolle says there somewhere in [1,3] there is a number c with \[f'(c)=0\] set \[3x^2-12x+11=0\] solve for x

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Other answers:

that is where i am stuck, i got that far
use the quadratic formula if it does not factor
if that is too annoying, then cheat^2-12x%2B11%3D0

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