DERIVATIVES
CHAPTER 1: DIFFERENTIATION
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1. INTRODUCTION TO DERIVATIVES
A. TANGENTS
B. VELOCITIES
C. RATES OF CHANGE
D. DERIVATIVE OF A FUNCTION
E. LEFT-HAND AND RIGHT-HAND DERIVATIVES
F. DIFFERENTIABILITY AND CONTINUITY
–Activity: Linear Approximation
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2. TECHNIQUES OF DIFFERENTIATION
A. BASIC DIFFERENTIATION RULES
B. THE PRODUCT AND THE QUOTIENT RULES
C. THE CHAIN RULE
D. HIGHER ORDER DERIVATIVES
–Activity: Linear Motion
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3. DERIVATIVES OF ELEMENTARY FUNCTIONS
A. DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS
1. Exponential Functions
2. Logarithmic Functions
3. Logarithmic Differentiation
B. DERIVATIVES OF TRIGONOMETRIC FUNCTIONS
C. DERIVATIVES OF SPECIAL FUNCTIONS
1. Absolute Value Functions
2. Sign Functions
3. Floor Functions
D. IMPLICIT DIFFERENTIATION
E. DERIVATIVES OF PARAMETRIC FUNCTIONS
F. DERIVATIVES OF INVERSE TRIGONOMETRIC FUNCTIONS
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CHAPTER 2: APPLICATIONS OF THE DERIVATIVE
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1. L’HOSPITAL’S RULE
A. THE INDETERMINATE FORM 0/0
B. THE INDETERMINATE FORM ∞ /∞
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2. APPLICATIONS OF THE FIRST DERIVATIVES
A. INTERVALS OF INCREASE AND DECREASE
B. MAXIMUM AND MINIMUM VALUES
1. Absolute and Local Maximum and Minimum
2. Finding the Local Extrema
3. The First Derivative Test
4. Finding the Absolute Extrema
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3. APPLICATIONS OF THE SECOND DERIVATIVES
A. CONCAVITY
B. THE SECOND DERIVATIVE TEST
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4. OPTIMIZATION PROBLEMS
–Activity: Refraction of Light
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5. PLOTTING GRAPHS
A. ASYMPTOTES
B. CURVE PLOTTING Vid 0 ,