Question

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

Answer 1

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
\[f'(x)=\frac{f(1)-f(-2)}{3}\]

Answer 2

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

Answer 3

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"