Calculus
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  • Version #1
    • Unit 0 >
      • 0.1 Summer Packet
      • 0.2 Calculator Skillz
    • Unit 1 >
      • 1.1 Can Change Occur at an instant
      • 1.2 Defining Limits and Using Limit Notation
      • 1.3 Limit Values from Graphs
      • 1.4 Limit Values from Tables
      • 1.5 Determining Limits Using Algebraic Properties
      • 1.6 Determining Limits Using Algebraic Manipulation
      • 1.7 Selecting Procedures for Determining Limits
      • 1.8 Determining Limits Using the Squeeze Theorem
      • 1.9 Connecting Multiple Representations of Limits
      • mid-Unit 1 Review
      • 1.10 Exploring Types of Discontinuities
      • 1.11 Defining Continuity at a Point
      • 1.12 Confirming Continuity Over an Interval
      • 1.13 Removing Discontinuities
      • 1.14 Infinite Limits and Vertical Asymptotes
      • 1.15 Limits at Infinity and Horizontal Asymptotes
      • 1.16 Intermediate Value Theorem
      • End of Unit 1 Review
    • Unit 2 >
      • 2.1 Defining Average and Instantaneous Rate of Change at a Point
      • 2.2 Defining the Derivative of a Function and Using Derivative Notation
      • 2.3 Estimating Derivatives of a Function at a Point
      • 2.4 Connecting Differentiability and Continuity
      • 2.5 Applying the Power Rule
      • 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
      • 2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
      • 2.8 The Product Rule
      • 2.9 The Quotient Rule
      • 2.10 Derivatives of tan(x), cot(x), sec(x), csc(x)
      • Unit 2 Review
    • Unit 3 >
      • 3.1 The Chain Rule
      • 3.2 Implicit Differentiation
      • 3.3 Differentiating Inverse Functions
      • 3.4 Differentiating Inverse Trigonometric Functions
      • 3.5 Selecting Procedures for Calculating Derivatives
      • 3.6 Calculating Higher-Order Derivatives
      • Unit 3 Review
    • Unit 4 >
      • 4.1 Interpreting the Meaning of the Derivative in Context
      • 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
      • 4.3 Rates of Change in Applied Contexts Other Than Motion
      • 4.4 Introduction to Related Rates
      • 4.5 Solving Related Rates Problems
      • 4.6 Approximating Values of a Function Using Local Linearity and Linearization
      • 4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms
      • Unit 4 Review
    • Unit 5 >
      • 5.1 Using the Mean Value Theorem
      • 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
      • 5.3 Determining Intervals on Which a Function is Increasing or Decreasing.
      • 5.4 Using the First Derivative Test to Determine Relative Local Extrema
      • 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
      • 5.6 Determining Concavity of Functions over Their Domains
      • 5.7 Using the Second Derivative Test to Determine Extrema
      • mid-Unit 5 Review
      • 5.8 Sketching Graphs of Functions and Their Derivatives
      • 5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
      • 5.10 Introduction to Optimization Problems
      • 5.11 Solving Optimization Problems
      • 5.12 Exploring Behaviors of Implicit Relations
      • End of Unit 5 Review
    • Unit 6 >
      • 6.1 Exploring Accumulation of Change
      • 6.2 Approximating Areas with Riemann Sums
      • 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
      • 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
      • 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
      • Mid-Unit 6 Review
      • 6.6 Applying Properties of Definite Integrals
      • 6.7 The Fundamental Theorem of Calculus and Definite Integrals
      • 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
      • 6.9 Integrating Using Substitution
      • 6.10 Integrating Functions Using Long Division and Completing the Square
      • 6.11 Integration by Parts
      • 6.12 Integrating Using Linear Partial Fractions
      • 6.13 Evaluating Improper Integrals
      • 6.14 Selecting Techniques for Antidifferentiation
      • End of Unit 6 Review
    • Unit 7 >
      • 7.1 Modeling Situations with Differential Equations
      • 7.2 Verifying Solutions for Differential Equations
      • 7.3 Sketching Slope Fields
      • 7.4 Reasoning Using Slope Fields
      • 7.5 Approximating Solutions Using Euler’s Method
      • 7.6 General Solutions Using Separation of Variables
      • 7.7 Particular Solutions using Initial Conditions and Separation of Variables
      • 7.8 Exponential Models with Differential Equations
      • 7.9 Logistic Models with Differential Equations
      • Unit 7 Review
    • Unit 8 >
      • 8.1 Average Value of a Function on an Interval
      • 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
      • 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
      • 8.4 Finding the Area Between Curves Expressed as Functions of x
      • 8.5 Finding Area Between Curves Expressed as Functions of y
      • 8.6 Finding the Area Between Curves That Intersect at More Than Two Points
      • Mid-Unit 8 Review
      • 8.7 Volumes with Cross Sections: Squares and Rectangles
      • 8.8 Volumes with Cross Sections: Triangles and Semicircles
      • 8.9 Volume with Disc Method: Revolving Around the x- or y-Axis
      • 8.10 Volume with Disc Method: Revolving Around Other Axes
      • 8.11 Volume with Washer Method: Revolving Around the x- or y-axis
      • 8.12 Volume with Washer Method: Revolving Around Other Axes
      • 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
      • End of Unit 8 Review
    • Unit 9 >
      • 9.1 Defining and Differentiating Parametric Equations
      • 9.2 Second Derivatives of Parametric Equations
      • 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
      • 9.4 Defining and Differentiating Vector-Valued Functions
      • 9.5 Integrating Vector-Valued Functions
      • 9.6 Solving Motion Problems using Parametric and Vector-Valued Functions
      • 9.7 Defining Polar Coordinates and Differentiating in Polar Form
      • 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve
      • 9.9 Finding the Area of the Region bounded by Two Polar Curves
      • Unit 9 Review
    • Unit 10 >
      • 10.1 Defining Convergent and Divergent Infinite Series
      • 10.2 Working with Geometric Series
      • 10.3 The nth Term Test for Divergence
      • 10.4 Integral Test for Convergence
      • 10.5 Harmonic Series and p-series
      • 10.6 Comparison Tests for Convergence
      • 10.7 Alternating Series Test for Convergence
      • 10.8 Ratio Test for Convergence
      • 10.9 Determining Absolute or Conditional Convergence
      • Mid-Unit 10 Review
      • 10.10 Alternating Series Error Bound
      • 10.11 Finding Taylor Polynomial Approximations of Functions
      • 10.12 Lagrange Error Bound
      • 10.13 Radius and Interval of Convergence of Power Series
      • 10.14 Finding Taylor or Maclaurin Series for a Function
      • 10.15 Representing Functions as a Power Series
      • End of Unit 10 Review
  • Version #2
    • Derivatives >
      • Unit 0 - Calc Prerequisites >
        • 0.1 Things to Know for Calc
        • 0.2 Summer Packet
        • 0.3 Calculator Skillz
      • Unit 1 - Limits >
        • 1.1 Limits Graphically
        • 1.2 Limits Analytically
        • 1.3 Asymptotes
        • 1.4 Continuity
        • Review - Unit 1
      • Unit 2 - The Derivative >
        • 2.1 Average Rate of Change
        • 2.2 Definition of the Derivative
        • 2.3 Differentiability
        • Review - Unit 2
      • Unit 3 - Basic Differentiation >
        • 3.1 Power Rule
        • 3.2 Product & Quotient Rule
        • 3.3 Velocity/Rates of Change
        • 3.4 Chain Rule
        • 3.5 Trig Derivatives
        • Review - Unit 3
      • Unit 4 - More Derivatives >
        • 4.1 Exp and Log Derivatives
        • 4.2 Inverse Derivatives
        • 4.3 L'Hopitals Rule
        • Review - Unit 4
      • Unit 5 - Curve Sketching >
        • 5.1 Extreme Values
        • 5.2 First Derivative Test
        • 5.3 Second Derivative Test
        • Review - Unit 5
      • Unit 6 - Implicit Differentiation >
        • 6.1 Implicit Differentiation
        • 6.2 Related Rates
        • 6.3 Optimization
        • Review - Unit 6
      • SEMESTER REVIEW
    • Integrals >
      • Unit 7 - Approximation Methods >
        • 7.1 Rectangular Approximation
        • 7.2 Trapezoidal Approximation
      • Unit 8 - Integration >
        • 8.1 Definite Integral
        • 8.2 First Fundamental Theorem of Calculus
        • 8.3 Antiderivatives
        • Review - Unit 8
      • Unit 9 - FTC Part 2 >
        • 9.1 The 2nd FTC
        • 9.2 Trig Integrals
        • 9.3 Average Value
        • 9.4 Net Change
        • Review - Unit 9
      • Unit 10 - More Integrals >
        • 10.1 Slope Fields
        • 10.2 u Sub Indefinite Integral
        • 10.3 u Sub Definite Integral
        • 10.4 Separation of Variables
        • Review - Unit 10
      • Unit 11 - Area and Volume >
        • 11.1 Area Between Curves
        • 11.2 Solids of Revolution (Discs)
        • 11.3 Solids of Revolution (Washers)
        • 11.4 Perpendicular Cross Sections
        • Review - Unit 11
  • FRQ
    • 2022 AB
    • 2022 BC
  • Teacher Resources

2.3 Differentiability

Packet

c_2.3_packet.pdf
File Size: 516 kb
File Type: pdf
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Practice Solutions

c_2.3_solutions.pdf
File Size: 463 kb
File Type: pdf
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Corrective Assignment

c_2.3_ca1.pdf
File Size: 266 kb
File Type: pdf
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Below is a walkthrough for the test prep questions.  Try them ON YOUR OWN first, then watch if you need help.  A little suffering is good for you...and it helps you learn.

This lesson contains the following Essential Knowledge (EK) concepts for the *AP Calculus course.  Click here for an overview of all the EK's in this course.
EK 1.2B1
EK 2.1A4

EK 2.1A5
EK 2.2A2
EK 2.2A3

EK 2.2B1
EK 2.2B2
EK 2.3B2
EK 2.4A1

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