Question

determine wheter the mean value theorem can be applied to f(x) = sqrt(x-6) on the interval [11,23]. If it can be applied, find all values of c in the interval (11,23) such that f(c) = f(b) - f(a) / (b-a)

Answer 1

First ask if the function is continuous on that interval, then ask if the function is differentiable on that interval. If these two conditions are met, then you may apply the mean value theorem.

Answer 2

and the answer is yes, it is, so you only need to find \(f(11)=\sqrt{11-6}=\sqrt{5}\), \( f(23)=\sqrt{17}\)
\[\frac{f(23)-f(11)}{23-11}=\frac{\sqrt{17}-\sqrt{5}}{12}=\frac{1}{2\sqrt{x-6}}\] but i am not sure how you are supposed to solve that

Answer 3

Cross multiplication is useful here.