Calculus I

CHAPTER8

The Difference Quotient

In This Chapter

• Creating a tangent from scratch
• How limits can calculate slope
• “Secant you shall find” the tangent line
• Both versions of the difference quotient

Although limits are important to the development of calculus and are the only topic we have even discussed so far, they are about to take a backseat to the two major topics comprising what most people call “calculus”: derivatives and integrals. It would be rude (and actually mathematically inaccurate) to simply start talking about derivatives without describing their relationship to limits.

Brace yourself. This chapter describes the solution ...