Question

Consider the function f(x)=3/x.

a. Determine an expression, in terms of a and h, for the average rate of change between the points (a,f(a)) and ( a + h, f(a+h) ) for the function . Show all steps needed to find a simplified algebraic expression.

b. Using your expression from (a), determine the average rate of change from x = -1 to x = 2. (no decimal values)

Answer 1

as always, the average rate of change is just the slope between the two points:

∆y/∆x = (f(a+h)-f(a))/h
Now just plug in a=-1, h=3

Answer 2

oh, yeah. with f(x) = 3/x,
∆y = 3/(a+h) - 3/a = -3h/(a(a+h))

Answer 3

how did you get h=3? and isnt it (-3h/(a(a+h)))/h

Answer 4

h is x2-x1, the change in x