1. ## Rolle's Theorem

Could someone please walk me through how I use Rolle's Theorem to find c for:

f(x) = x^3 - x^2 - 2x + 7

[ 0 , 2 ]

Sorry about the formatting, I don't know how to write latex code.

2. Notice $f(0)=f(2)$ so Rolle's theorem gives a $c\in [0,2]$ with $f'(c)=0$. If you want the value of such a c, notice $f'(x)=3x^2-2x-2$ and solve this quadratic polynomial.

3. So basically f'(c) = 0 so i set f'(x) = 0 and solve and the answer is c? So the answer is 1.2153 because -0.5486 is not on the interval [0,2]. Right?

4. If they are the solutions then the logic is fine.