Topic 1: First Derivatives, Extrema, and Curve Sketching

• • Intervals of Increasing and Decreasing – The Main Idea
  • Relative Extrema of a Power Function Example – continued below in Topic 2
  • Relative Extrema of a Product Function Example – continued below in Topic 2
  • Sketching f given f’
  • Analyzing f given f’

(MTH 263 only)

• • Analyzing f(x) = x^(1/x) Using Derivatives
  • Indeterminate Forms – The Main Idea
  • Logarithmic Techniques using L’Hospital’s Rule
  • Using L’Hospital’s Rule with Logs
  • Using L’Hospital’s Rule with Trig Functions
  • Another Example Using L’H Rule with Trig Expressions

Topic 2: Second Derivatives, Extrema, Concavity, and Curve Sketching

• • Concavity – The Main Idea
  • The Second Derivative Test for Extrema – The Main Idea
  • Concavity of a Power Function Example (continued)
  • Concavity of a Product Function Example (continued)
  • Finding Extrema and Concavity Example
  • Graphing f ‘(x) given the graph of f(x)
  • Sketching a function with the given properties
  • Sketching a function with the given derivative properties
  • Sketching a function with the given properties (another one!)
  • Curve Sketching (Ex.2)
  • Curve Sketching with e

Topic 3: Asymptotes and Rational Functions

• • Analyzing a Rational Function with H.A. at y = 0
  • Analyzing a Rational Function with a Slant Asymptote
  • Analyzing a Rational Function with a Hole
  • Analyzing a Logistic Function
  • Analyzing a Surge Function – Example

Topic 4: Optimization-Finding Absolute Max and Min Values

• • Absolute Extrema – The Main Idea
  • Finding the Absolute Extrema of a Function – Example
  • Maximizing Profit – Example
  • Maximum Drug Concentration – Example
  • Optimizing Area after Cutting a Wire

(MTH 263 only)

• • • Find the Absolute Extrema of a cosecant function
    • Find the Absolute Extrema of a Trig Function

Topic 5: Optimization Applications

• • Optimization – The Main Idea
  • Maximizing the Volume of a Box
  • Maximizing Profit at a Hotel
  • Maximizing Surface Area of a Cylinder
  • Maximizing the Volume of a Cone

(MTH 263 only)

• • Maximizing an Isosceles Triangle and Semicircle

Topic 6: Marginals and Differentials

• • Marginal Analysis – The Main Idea
  • Marginal Analysis (continued) with Example
  • Marginal Profit Example
  • Deltas and Differentials – The Main Idea
  • Approximating a Cube Root using Differentials
  • Tolerance Example

Topic 7: Elasticity of Demand (MTH 261 only)

• • Elasticity – The Main Idea
  • Elasticity Example – Linear Demand Function
  • Elasticity Example  Exponential Demand Function

Topic 8: Implicit Differentiation

• • Implicit Differentiation – The main idea
  • Implicit Differentiation with The Product Rule
  • Implicit Differentiation with e and ln
  • Second Derivative using Implicit Differentiation
  • Second Derivative using Implicit Differentiation – Harder Ex.
  • Finding A Derivative Two Ways

(MTH 263 only)

• • Finding the Tangent Lines to an Ellipse Passing Through a Given Point
  • Implicit Differentiation with a Trig Function

Topic 9: Related Rates

• • Related Rates – The main idea
  • Related Rates with Cost, Revenue, Profit
  • Related Rates – Stock Problem
  • Related Rates – Ladder Problem
  • Related Rates – Conical Pile Problem