The horizontal change
is shown by the red arrow, and the vertical change
is shown by the turquoise arrow. The average rate of change is shown by the slope of the orange line segment. The output changes by –3 while the input changes by 3, giving an average rate of change of
After picking up a friend who lives 10 miles away and leaving on a trip, Anna records her distance from home over time. The values are shown in
[link] . Find her average speed over the first 6 hours.
t (hours)
0
1
2
3
4
5
6
7
D (
t ) (miles)
10
55
90
153
214
240
292
300
Here, the average speed is the average rate of change. She traveled 282 miles in 6 hours.
The
electrostatic force
measured in newtons, between two charged particles can be related to the distance between the particles
in centimeters, by the formula
Find the average rate of change of force if the distance between the particles is increased from 2 cm to 6 cm.
We are computing the average rate of change of
on the interval
The average rate of change is
newton per centimeter.
Finding an average rate of change as an expression
Find the average rate of change of
on the interval
The answer will be an expression involving
in simplest form.
We use the average rate of change formula.
This result tells us the average rate of change in terms of
between
and any other point
For example, on the interval
the average rate of change would be
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
