Sec 2.2 Basic Differentiation Rules and Rates of Change

Essential Questions:
*How do you utilize the various differentiation rules to determine the derivative of a function?
Constant rule, Power rule, Constant multiple rule, Sum and difference rule, Trigonometric derivatives (Sine and Cosine)
*How do instantaneous and average rates of change compare?
*What do we mean by instantaneous rate of change?

*Can you use rates of change to determine the velocity, speed, acceleration, and jerk of an object?

Objectives:

(1) Use the Constant Rule, Power Rule,Constant Multiple Rule, and Sum and Difference Rules as short cuts to differentiate functions.
(2) Find higher order derivatives and apply them to problem such as speed, velocity, and acceleration.

October 5 - 9, 2009

Monday, 10/5--Section 2.2 (pgs. 107 - 112)
*Rules for Differentiation: the Constant Rule, the Power Rule, the Constant Multiple Rule, the Sum and Difference Rules, Derivatives of Sine and Cosine Functions
*Homework Assignment: page 115 - 118 #3-21 odd, 39 - 53 odd

Tuesday, 10/6--Section 2.2 part 1 (cont'd)
*Homework Review/Q & A
*Practice with rules for differentiation
*Classwork: Worksheet 2.2
*Overview of 2.2, part 2 using the "How Do We Measure Speed?" handout from 10/2;

Wednesday, 10/7--Section 2.2 (pages 113 - 114)
*Rates of Change: the position function, average velocity and instantaneous velocity
*Discuss "Try These" problems from "Speed" packet
*Homework Assignment: Average Velocity and Instantaneous Velocity worksheet

Thursday, 10/8--Section 2.2 Review
*HW Review/Q&A
*Review for Test on 2.1 and 2.2 (Test will be administered Monday)
*Homework Assignment: page 116 - 118 #57-65 odd, 67, 68, 89, 91-96 all

Friday, 10/9--NO SCHOOL

Sec 2.1 Video: Sketching the Derivative of a Function

Sec 2.1 Video: The Graph of the Derivative

What is the Meaning of the Derivative?

September 28 - October 2

Monday, 9/28--Section 2.1--The Definition of the Derivative and the Tangent Line *Submit Chapter 1 Spiral worksheet
*Essential Question: What is the relationship between the slope of a secant line to a curve and the slope of a tangent to a curve?
*Find the derivative using the limit process
*Find the slope of the line tangent to a curve
*Homework Assignment: page 104 #5-21 odd

Tuesday, 9/29--Section 2.1 (Cont'd)
*Essential Question: What is the derivative of a function at a point and how is it related to the tangent line? How can we determine if a function is differentiable over an interval?
*Calculus Phobe video on the derivative: http://www.calculus-help.com/funstuff/tutorials/derivatives/deriv01.html
*Homework Review/Q&A
*Using GC to find the derivative at a point
*The alternative form of the derivative
*Homework Assignment: page 104 #12-24 even, 71, 77,79; Read pages 101-103


Wednesday, 9/30--GHSGT Writing--NO PERIOD 2
We will still have the Calculus Study Group afterschool from 3:50 - 5:00 pm! Show up if you need help.

Thursday, 10/1--Sec 2.1, part 3...Differentiablity and Continuity
*HW Review
*Investigate the relationship between differentiability and continuity
*Sketch the graph of f'(x) given f(x)
*Homework Assignment: page 104 #37-40, 81-87 odd
*Study for a quiz on section 2.1 (this will be a homework quiz; the quiz questions will come from the homework assignments for this section)

Friday, 10/2--Sec 2.1 summary
*Recap differentiability and continuity
*Video on sketching the derivative
*Sec 2.1 Homework Quiz
*Homework Assignment: "How Do We Measure Speed" handout; read pages 70-74; complete the "Try These" problems #1-6

Section 2.1 Video: The Definition of the Derivative

Section 2.1 Video: Finding the Equation of a Tangent Line

TI Graphing Calculator

Here is a site that lets you download a TI Emulator to your computer like the one I use in class. This will be helpful for those of you who still do not have a graphing calculator at home!!http://dkarasmath.googlepages.com/tiprograms

Please be advised that I am not associated with the information contained on the page for the link. I found it through a search. I am not responsible and will not be liable for any information found on the page link.