Page 107 - Calculus Workbook For Dummies
P. 107
Chapter 7
Analyzing Those Shapely Curves
with the Derivative
In This Chapter
Mum’s the word: Minimum, maximum, extremum
Concavity and inflection points
The nasty mean value theorem
his chapter gives you lots of practice using the derivative to analyze the shape of
Tcurves and their significant features and points. Don’t forget: The derivative tells you
the slope of a curve, so any problem involving anything about the slope or steepness of a
curve is a derivative problem.
The First Derivative Test and Local Extrema
One of the most common applications of the derivative employs the simple idea that at the
top of a hill or at the bottom of a valley, you’re neither going up nor down; in other words,
there’s no steepness and the slope — and thus the derivative — equals zero. You can there-
fore use the derivative to locate the top of “hills” and the bottom of “valleys,” called local
extrema, on just about any function by setting the derivative of the function equal to zero
and solving.
