Page 285 - Calculus Workbook For Dummies

Chapter 15

Ten Things You Better Remember

aboutDifferentiation

In This Chapter

Psst, over here
The difference quotient
Extrema, concavity, and inflection points
The product and quotient rules

n this chapter, I give you ten important things you should know about differentiation.
IRefer to these pages often. When you get these ten things down cold, you’ll have taken a
not-insignificant step toward becoming a differentiation expert.

The Difference Quotient

The formal definition of a derivative is based on the difference quotient:
f x + h - ^h f xh rise
^
x =
f l ^ h lim ; this says basically the same thing as slope= .
h " o h run
The First Derivative Is a Rate

A first derivative tells you how much y changes per unit change in x. For example, if y is in
miles and x is in hours, and if at some point along the function, y goes up 3 when x goes over 1,
you’ve got 3 mph. That’s the rate and that’s the derivative.

The First Derivative Is a Slope

In the previous example, when y goes up 3 (the rise) as x goes over 1 (the run), the slope
(rise/run) at that point of the function would be 3 of course. That’s the slope and that’s the
derivative.