Math Analysis
Derivative Units
Unit D-1 Review of Factoring Polynomials
- Standard D1: Factor Quadratic Equations and Reduce Rational Expressions
Agenda
- Factor Quadratic Equations
- Reduce Rational Expressions by Factoring
Unit D-2 Introduction to Limits
- Standard D2: Evaluate limits involving the indeterminate form 0/0
Agenda
- Graphing the "hole" on the calculator
- Finding the y coordinate of the "hole"
- Simplifying Rational Expressions to find the Limit
Unit D-3 Introduction to the Derivative
- Standard D3a: Write and sketch a secant line using the slope equation
- Standard D3b: Write and sketch a tangent line using the limit of a slope equation (derivative definition at a point)
- Standard D3c: Use secant and tangent line slopes to find average and instantaneous velocity
Agenda
- Graphing the secant line
- Graphing the tangent line
- Applying secant and tangent line slopes to problems involving projectile motion
Unit D-4 The Power Rule
- Standard D4: Find the derivative of a polynomial function using the Power Rule
Agenda
- Using the Power Rule to Differentiate a Polynomial
Unit D-5 Tangent Line Equations
- Standard D5: Find the equation of a tangent line using the Power Rule
Agenda
- Using the Power Rule to find the slope of a curve at a given point
- Using the equation of a line with the derivative to find a tangent line
- Finding the value(s) of x at which the slope of a tangent line is 0
Unit D-6 Find the Critical and Exreme Values of a Polynomial Function
- Standard D6a: Find the relative max/min of a polynomial function using the Power Rule
- Standard D6b:Use sign patterns for the derivative to find intervals of increasing and decreasing of a function
Agenda
- Finding the zeros of the derivative
- Using sign patterns of the derivative to determine the behavior of a function
- Identifying a critical point as minimum, maximum, or neither.
- Find the extreme values
Unit D-7 Find the instantaneous velocity using the Power Rule
- Standard D7:Find the instantaneous velocity of a polynomial function of position using the Power Rule
Agenda
- Using the Power Rule to find the derivative of a position function
- Finding the value(s) of t at which an object stops and/or changes direction
- Using the velocity to find the direction of motion of a particle
- Screencast
- Powerpoint
- PDF Slides
- Desmos Activity