mean value theorem

[Guest]

f(1)=2- , f(-1)=0 f(x)=x^3-x^2-2x on [-1,1], find all values of c in [-1,1] satisfing the conlusion of the mean value theorem

f'(x)=3x^2-2x-2 set that equal to -1 to find c in [-1,1]

3x^2-2x-2=-1 where do I go from here?

 

[galactus]

\(\displaystyle 3c^{2}-2c-2=\frac{f(b)-f(a)}{b-a}\), over the interval [a,b].

In your case, [-1,1].

Solve for c.