Consider the function #f(x) = 1/x# on the interval #[4, 11]# and answer the following?
Consider the function #f(x) = 1/x# on the interval #[4, 11]# .
(A) Find the average or mean slope of the function on this interval.
(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 a box.
Consider the function
(A) Find the average or mean slope of the function on this interval.
(B) By the Mean Value Theorem, we know there exists a
1 Answer
See below.
Explanation:
A)
The Average Rate of change over an interval #[a,b] is given by:
From example:
B)
The mean value theorem:
We already have the average rate of change
So we need to differentiate
For interval