Hi, I am stuck to a certain point on this problem:

1. Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(c)=0.

f(x)=(x-1) (x-2) (x-3), [1,3]

I know Rolle's Theorem can be applied since f is continuous along the interval of [1,3] and differentiable along that interval as well.

f(x) = x[sup:cghctzop]3[/sup:cghctzop]-6x[sup:cghctzop]2[/sup:cghctzop]+11x-6

f'(x) = 3x[sup:cghctzop]2[/sup:cghctzop]-12x+11

I'm stuck after that, how would you find the values of c? Thanks!

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