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.

Question

anonymous · Answer

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

anonymous · Answer

since 
$$f(1)=f(3)=0$$ and since any polynomial is differentiable you can use rolle

anonymous · Answer

$$f(x)=x^3-6 x^2+11 x-6$$
$$f'(x)=3x^2-12x+11$$ 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

anonymous · Answer

that is where i am stuck, i got that far

anonymous · Answer

use the quadratic formula if it does not factor

anonymous · Answer

if that is too annoying, then cheat http://www.wolframalpha.com/input/?i=3x^2-12x%2B11%3D0

anonymous · Answer

-b+-sqrt(b^2-4ac)/2a?

anonymous · Answer

yup