Question

HELP FIND THE AVERAGE RATE OF CHANGE

Answer 1

The average rate of change of a function
`f(x)` as
`x` varies from
`x=a` to
`x=b` is given by the so-called difference quotient

`(f(b) - f(a))/(b - a)`

If we plot
`f(x)`, this difference quotient would correspond to the slope of the line through two points
`(a,f(a))` and
`(b,f(b))` and intersecting with the curve
`y=f(x)`.

(a) The average rate of change of height from 0 to 6.6 seconds is

`(H(6.6) - H(0))/(6.6 - 0)`

and is measured in m/s.

Consult the table for the values of
`H(t)` - it tells us
`H(0)=0` and
`H(6.6)=198`. So the average rate of change of height in this time is

`(198 - 0)/(6.6 - 0) (\rm m)/(\rm s) = \boxed{30(\rm m)/(\rm s)}`

(b) Similarly, the average rate of change of height from 8.8 to 13.2 seconds is

`(H(13.2) - H(8.8))/(13.2-8.8) (\rm m)/(\rm s) = (0 - 44))/(4.4) (\rm m)/(\rm s)= \boxed{-10 (\rm m)/(\rm s)}`