Calculus For Dummies, 2nd Edition

Chapter 13

More Differentiation Problems: Going Off on a Tangent

In This Chapter

Tangling with tangents

Negotiating normals

Lining up for linear approximations

Profiting from business and economics problems

In this chapter, you see three more applications of differentiation: tangent and normal line problems, linear approximation problems, and economics problems. The common thread tying these problems together is the idea of a line tangent to a curve — which should come as no surprise since the meaning of the derivative of a curve is the slope of the tangent line.

Tangents and Normals: Joined at the Hip

By now you know what a line tangent to a curve looks like — if not, one or both of us has definitely dropped the ball. A normal line is simply a line perpendicular to a tangent line at the point of tangency. Problems involving tangents and normals are common applications of differentiation.

The tangent line problem

I bet there have been several times, just in the last month, when you’ve wanted to determine the location of a line through a given point that’s tangent to a given curve. ...