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