[tex] \frac{f(2)-f(1)}{2-1}= \frac{2^3+2-9-(1^3+1-9)}{1}=8+2-9-1-1+9=8
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derivative of f(x) =3x^2+1,3x^2+1=8,3x^2=7,x= \sqrt \frac{7}{3} [/tex] which supports the mean value theorem, you want even better news if the function is a polynomial it will always follow the mean value theorem
