Page 150 - Calculus Workbook For Dummies

134 Part III: Differentiation

4
2
13. s t = t + t - t 14. s t = t + 1
^ h
^ h
2
t + 4
Solve It Solve It

Make Sure You Know Your Lines:

Tangents and Normals

In everyday life, it’s perfectly normal to go off on a tangent now and then. In calculus,
on the other hand, there is nothing at all normal about a tangent. You need only note a
couple points before you’re ready to try some problems:

At its point of tangency, a tangent line has the same slope as the curve it’s tan-
gent to. In calculus, whenever a problem involves slope, you should immediately
think derivative. The derivative is the key to all tangent line problems.
At its point of intersection to a curve, a normal line is perpendicular to the tangent
line drawn at that same point. When any problem involves perpendicular lines,
you use the rule that perpendicular lines have slopes that are opposite recipro-
cals. So all you do is use the derivative to get the slope of the tangent line, and
then the opposite reciprocal of that gives you the slope of the normal line.
Ready to try a few problems? Say, that reminds me. I once had this problem with my
carburetor. I took my car into the shop, and the mechanic told me the problem would
be easy to fix, but when I went back to pick up my car . . . Wait a minute. Where was I?