Let f(x)=\dfrac{1}{x-2}f(x)=
x−2
1

f, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, x, minus, 2, end fraction.
can we use the mean value theorem to say the equation f'(x)=\dfrac12f
′
(x)=
2
1

f, prime, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction has a solution where 1< x< 41