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:


`(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:


`(f(6)-f(1))/(6-1) \\ \\ = (-ln(6)-(-ln(1)))/(5) = (-ln(6)-0)/(5) \\ \\ = (-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