CHAPTER 9
Big Idea 2: Derivatives
More Applications of
Derivatives
IN THIS CHAPTER
Summary:Finding an equation of a tangent is one of the most common questions on
the AP Calculus BC exam. In this chapter, you will learn how to use derivatives to find
an equation of a tangent, and to use the tangent line to approximate the value of a
function at a specific point. You will also learn to find derivatives of parametric, polar,
and vector functions, and to apply derivatives to solve rectilinear motion problems.
Key Ideas
KEY IDEA !Tangent and Normal Lines
!Linear Approximations
!Motion Along a Line
!Parametric, Polar, and Vector Derivatives9.1 Tangent and Normal Lines
Main Concepts:Tangent Lines, Normal LinesTangent Lines
If the functionyis differentiable atx=a, then the slope of the tangent line to the graph of
yatx=ais given asm(tangent atx=a)=
dy
dx∣
∣∣
∣
x=a.
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