- #1
msc8127
- 23
- 0
Homework Statement
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
Homework Equations
f(x) = (x-1)(x-2)(x-3) with the interval being [1,3]
The Attempt at a Solution
the function is continuous on [1,3] and differentiable on (1,3)
f(1) = 0 and f(3) = 0 so f(1) = f(3)
f'(x) = 3x^2 - 12x + 11
now I need to find the point in [1,3] with slope 0 so I set f'(x) = 0.
I know from here I'm supposed to get c values of (6 - sqrt 3) / 3 and (6 + sqrt 3) / 3 however the algebra to get me to this point is eluding me.
Can someone please point of the obvious for me?
Thanks