A function is given. Determine the average rate of change of the function between the given values of the variable.

Question

A function is given. Determine the average rate of change of the function between the given values of the variable.

f(t) = 9 / t ; t = a, t = a + h

Answer 1

We need [ f(a+h)-f(a) ] / ( a+h - a)

= [ f(a+h)-f(a) ] / h

We got

f(a) = 9/a

and

f(a+h) = 9/(a+h)

So then:

f(a+h) - f(a) = 9/(a+h) - 9/a

= [9a - 9(a+h)] / a(a-h)

= [ 9a - 9a - 9h]/ (a^2-ah)

= -9h/(a^2-ah)

Dividing by

h:

-9/(a^2 - ah)