how do you solve: f(x)= x^2, [-2,1] with the mean value theorem

Question

anonymous · Answer

i am going to make a guess that this means 
"show that f satisfies the hypothesis of the mean value theorem, and find the c for which 
$$f'(x)=\frac{f(1)-f(-2)}{3}$$

anonymous · Answer

That's a nice guess satellite. I'm sure you meant that $f'(c)=\frac{f(1)-f(-2)}{3}$, where $-2\le c \le 1$.

anonymous · Answer

yes that is what i meant.  these questions always annoy me because it turns a theorem into a calculation, as if students are too dumb to understand and if - then statement. of course mvt doesn't say "solve for c"