Consider the function f(x) = 1/x on the interval [ 4 , 11 ].

Question

(A) Find the average or mean slope of the function on this interval.
Average Slope =

(B) By the Mean Value Theorem, we know there exists a c in the open interval ( 4 , 11 ) such that f'( c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below.

List of values:

Answer 1

the mean slope is just (1/11 - 1/4)/(11-4) = -1/44

so, where is f'(x) = -1/44