Page 83 - Calculus Workbook For Dummies

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Chapter 5: Getting the Big Picture: Differentiation Basics

c. What’s the average velocity from t = 4 to t = 4.01? The answer is 24.03 miles/hour.

s ^ . 4 01 - ^h s 4h
. 4 01 =
Average Velocity 4 to
. 4 01 - 4
3 $ . 4 01 - $ 2
3 4
2
=
. 0 01
miles
= 24 .03
hour
l For the position function in problem 11, what’s the instantaneous velocity at t = 4? The answer
x =
is 24 miles/hour. Problem 8 gives you the derivative of this parabola, f l ^ h 6 x. The position
function in this problem is the same except for different variables, so its derivative is s t = t 6 .
l ^ h
miles
Plug in 4, and you get s 4 = 24 . Notice how the average velocities get closer and closer
l ^ h
miles hour
to 24 as the total travel time gets less and less and the ending time hones in on t = 4.
hour
That’s precisely how the difference quotient works as h shrinks to zero.