Final answer:
To find the value of b such that the average rate of change of f on the interval (2, b) is -(1/10), we need to first find the expression for the average rate of change of f. The value of b is 4/3.
Step-by-step explanation:
To find the value of b such that the average rate of change of f on the interval (2, b) is -(1/10), we need to first find the expression for the average rate of change of f.
The average rate of change of a function f on an interval (a, b) is given by the formula:
Average rate of change = (f(b) - f(a))/(b - a)
In this case, we have f(x) = 1/x. So, the average rate of change of f on the interval (2, b) is:
(1/b - 1/2)/(b - 2) = -1/10
To solve this equation, we can multiply through by 10(b-2) to get:
10(1/b - 1/2) = -1
Simplifying the equation, we get:
10 - 5b = -b + 2
6b = 8
b = 8/6 = 4/3