AP Calculus - NJCTL

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AP Calculus

Derivatives

20151103

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Table of Contents

Rate of Change Slope of a Curve (Instantaneous ROC) Derivative Rules: Power, Constant, Sum/Difference Higher Order Derivatives Derivatives of Trig Functions Derivative Rules: Product & Quotient Calculating Derivatives Using Tables Equations of Tangent & Normal Lines Derivatives of Logs & e Chain Rule Derivatives of Inverse Functions Continuity vs. Differentiability Derivatives of Piecewise & Abs. Value Functions Implicit Differentiation

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Why are Derivatives Important?

First, let's discuss the importance of Derivatives: Why do we need them?

a) What is the slope of the following function? b) What is the slope of the line graphed at right?

Teacher Notes

The idea students ab learned ab classes. Th math course finding slop prompted to should lead students. S that "there realize "the

c) Now, what about the slope of

???

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Derivatives Exploration

Exploration into the idea of being locally linear...

Click here to go to the lab titled "Derivatives Exploration: y = x2"

Teacher Notes

Lead stu having th

their ch slowly by little by lit

that e resemble that this f allow the curves in

th URL for L

apcalc

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Rate of Change

Return to Table of Contents

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Road Trip!

Consider the following scenario:

You and your friends take a road trip and leave at 1:00pm, drive 240 miles, and arrive at 5:00pm. How fast were you driving?

Teacher Notes

When st

? How ? Are you

? What should c velocity)

? How w

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position

Teacher Notes

Position vs. Time

Now, consider the following position vs. time graph:

t0

t1

time

t2 t3

Students derivatives w

are fam D

? What d (average ? What does

(instan

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