Rolle's Theorem

[ashleym]

Hello I'm trying to determine whether Rolle's Theorem can be applied to f(x)=x^3-6x^2+11x-6. I know that it satisfies all 3 rules, but I'm stuck trying to find the value(s) of c. I know i have to set f'(c)=0, but that's where I draw a mental blank. f'(x)= 3x^2-12x+11=0 brings me to 3x^2-12x=-11. Then I'm confused with what to do with the x^2 and the x. I can't seem to find a way to factor this or solve for x. Please help!

 

[mmm4444bot]

3x^2 - 12x + 11

That polynomial does not factor nicely; use the Quadratic Formula, to find its two roots.

x = 2 + sqrt(3)/3

or

x = 2 - sqrt(3)/3