Week of January 26th
Tuesday, Jan 27th: Section 3.1 – Linear Approximation
Objectives
- Find Linear Approximation equations.
- Use Linear Approximation to approximate the value of a function near the point of tangency.
Learning Materials
Section 3-1 Instructor Video: To be posted.
Thursday, Jan 29th: Section 3.7 - Optimization
Objectives
- Solve Optimization problems.
Learning Materials
Section 3-7 Instructor Video:
Friday, Jan 30th: Section 3.9 – Rates of Change in the Sciences
Objectives
- Solve Economics Application Problems
- Know how to find the “marginal cost” or “marginal profit”.
- Know how to find an “average cost” equation.
- Solve Charge/ Current / Circuit Application Problems
- Solve Particle Motion Problems
- Find velocity and acceleration functions, given a position function.
- Find the time values where the particle changes direction.
- Find total distance traveled over a time interval and distinguish this from net distance traveled.
- Find intervals where a particle is speeding up/slowing down.
Learning Materials
3.9: Rates of Change in the Sciences PPT
Week of January 19th
Review and Exam on Curve Sketching!
Week of January 12th
Tues, Jan 13th: Section 3.4 – Increasing and Decreasing Functions
Objectives
- Know how to find where a function is increasing and decreasing.
- Know how derivatives relate to increasing/decreasing functions (Theorem 4.1)
- Know and be able to use the first derivative test to determine whether a critical point yields a maximum, minimum, or neither.
Learning Materials
3.4 Instructor Video:
Thurs, Jan 15th: Section 3.5 – Concavity and the Second Derivative Test
Objectives
- Know what it means for a function to be concave up or concave down.
- Know how first and second derivatives relate to concavity.
- Know the definition of an inflection point and how to find one.
- Use the 2nd Derivative Test to find extrema.
- Determine whether to use the 1st or 2nd derivative test, depending on the problem.
Fri, Jan 16th: Section 3.6 – Overview of Curve Sketching
In this lesson, we put everything we learned in 3.3 – 3.5 together and sketch curves! Click below for a summary and a practice test.
Function Graphing Notes Summary
Function Graphing Practice Test
Week of January 5th
Thurs, January 8th: Section 3.3 - Maximum and Minimum Values
Objectives
- Know the definition of Absolute/Global Extrema
- Know the definition of local/relative extrema
- Know how to find Absolute Extrema on a closed interval (Extreme Value Method)
- Know how to find local extrema (find the critical numbers – x-values where the derivative equals zero or does not exist)
- Understand Fermat’s theorem (If f(c) is a local extremum, Then c is a crit number) and why it’s converse is false.
Learning Materials
3-3 Instructor’s Video:
Week of December 15th
Tues, Dec 16th and Thurs, Dec 18th: Section 3.8: Related Rates
Objectives:
- Solve a variety of Related Rates application problems.
Learning Materials:
Related Rates Problem Solving Template
Related Rates Video:
