Question

Find the average rate of change for the equation [1,6] f(x)=-ln(x)

Answer 1

The average rate of change for a function f(x) at two different values of x can be calculated by the following formula:

$\frac{f( x_{2})-f( x_{1})}{ x_{2} - x_{1} }$

We are to find the find the average rate of change of given function over the range [1,6], so,

$x_{1}=1 \\ x_{2}=6$

Using the values in above formula, we get:

$\frac{f(6)-f(1)}{6-1} \\ \\ = \frac{-ln(6)-(-ln(1))}{5} = \frac{-ln(6)-0}{5} \\ \\ = \frac{-ln(6)}{5}$

Thus the average rate of change for f(x) = -ln(x) for the interval [1,6] is given by the above expression