In Segment A of this course, students will understand how to find the continuity of basic algebraic and trigonometric functions by using their graphs, properties of limits by using continuity, the first and second derivative graphically and numerically. They will also learn the concept of differentiability and its effects on continuity.

PRE-REQUISITES: Pre-Calculus recommended

ESTIMATED COMPLETION TIME: 16-18 weeks or approximately 65 – 75 hours

MAJOR TOPICS AND CONCEPTS – SEGMENT A

A Library of Functions

  • Functions and change
  • Exponential Functions
  • New Functions from Old
  • Logarithmic Functions
  • Trigonometric Functions
  • Powers, Polynomials, and Rational Functions
  • Introduction to Continuity
  • Limits

Using the Derivative

  • Using First and Second Derivatives
  • Optimization
  • Families of Functions
  • Optimization, Geometry and Modeling
  • Applications to Marginality
  • Rates and Related Rates
  • L’Hopital’s Rule, Growth and Dominance
  • Parametric Equations

Differentiation

  • How Do We Measure Speed?
  • The Derivative at a Point
  • The Derivative Function and Interpretations of the Derivative
  • The Second Derivative
  • Differentiability

Short-cuts to Differentiation

  • Constant Multiple Rule
    o Sum and Difference Rule
    o Power Rule
  • Exponential Function Rule
  • Product Rule
    o Quotient Rule
  • Chain Rule
  • Trigonometric Function Rules
  • Inverse Trig Function Rules
  • Implicit Function Rules
  • Hyperbolic Function Rules
  • Approximating the values of a function near a particular value
  • Differentiable function rules and attributes of a function

LINKS TO FULL COURSE CURRICULUM MAPS

SEGMENT A