Find all numbers c that satisfy the conclusion of the mean value theorem for the following function and interval:$$f(x)=3x^2+2x+2 \tag{[-1,1]}$$so far I have $$f'(x)=6x+2$$$$6x+2=-1$$$$x=-1/2$$and$$6x+2=1$$$$x=-\frac{1}{6}$$I know both of these are wrong, and the written answer is 0, but I don't see how to get the correct answer.
[Math] Find all numbers that satisfy the mean value theorem
calculus
Best Answer
$$ f(1) = 7, f(-1) = 3 $$ Mean value theorem states, for some c in [a, b] with a < b, $$ f'(c) = \frac{f(b)-f(a)}{b-a}, $$ As, you mentioned, $$ f'(x) = 6x + 2 $$ Can you solve now?