Velocity, Acceleration, & Other Rates of Change
Average Rate of Change:
f(x + h) - f(x)
or s(t
+ D t) - s(t)
where s represents distance and t is time
h
D t
In other words, the average rate of change of distance with respect
to time is given by the second expression above. The average rate
of change of distance with respect to time is what we call average
velocity.
Instantaneous Rate of Change:
Higher Order Derivatives
Suppose f(x) = 3x4
Then f '(x) = 12x3
f
"(x)
= 36x2
f
'''(x)
= 72x
f(4)(x)
= 72
f(5)(x)
= 0
f(6)(x)
= 0
