Find the average or mean slope of the function on this interval.

Question

Consider the function f(x)=1/x on the interval [3,9]. Find the average or mean slope of the function on this interval. 

By the mean value theorem, we know there exists a c in the open interval (3,9) such that f^'(c) is equal to this mean slope. For this problem, there is only one c that works. What is it?

Answer 1

Here f'(x) is -1/x^2. Plugging in c that's -1/c^2 equal to (1/9-1/3)/6 or -2/9/6=-1/27. So c is square root of 27.