Question

Using the Average Rate of Change of a Function formula, how do I solve g(x)=1/x; x=1, x=a?

Answer 1

Using the Average Rate of Change of a Function formula, how do I solve $g(x) = 1 / x; x = 1, x = a$?

Solution

The average rate of change is

$$\frac {g (b) - g (a)}{b - a} = \frac {\frac {1}{b} - \frac {1}{a}}{b - a} = \frac {a - b}{a b (b - a)} = - \frac {1}{a b} = - \frac {1}{a},$$

where $g(x) = \frac{1}{x}, a = a, b = 1.$