1. Fall wk 6 – Tues.Nov.04 Welcome, roll, questions, announcements
Calculus Ch.2: Concept of Derivative
2.1: How do we measure speed?
2.2: Limits
2.3: Derivative at a point
VOTE today!
Energy Systems, EJZ

2. Concept of a derivative
You have already encountered derivatives.
They describe the rate of change of a
dependent variable (e.g. position) on an independent variable (e.g. speed)
Calculus lets you describe rates of change at any point in a changing function.
Your questions and key points about Ch.2 …

3. Example of a derivative: oil production
Cumulative production vs time
When is cumulative production increasing most rapidly? a, b, or c
When is the production rate greatest? a, b, or c

4. Oil production rate = production/time
When is production rate increasing most rapidly? a, b, or c
When does production rate peak? a, b, or c
When does production rate start to decline? a, b, or c

5. 2.1: How do we measure speed v?
vaverage= slope over an interval = Dx/Dt
vinstantaneous= slope of tangent line at a point
vinstantaneous = lim Dx/Dt as Dx0

6. 2.1 continued Practice: teams do 2.1 #1-4 Discuss Ex.4 p.60
Conceptests

7. 2.1 Finding limits algebraically
Practice with Ex. 6, p.61; Teams do #5-8
Set up #17 together, finish 2.1 Conceptests

8. 2.2: Limits
Definition: lim(xc) f(x) = L
Ex.1 p.63:

9. 2.2: Limits: properties and practice
Teams do Ex.3, 4, 7 (p.65-67) or #15-19

10. 2.3: Derivative at a point

11. 2.3: Derivative at a point: practice
Teams practice with Ex.3-7; Conceptests
Three ways to find the derivative=slope:
Numerically (approximate)
Graphically (intuitive)
Analytically (exact)
Compute the derivative f ’=df/dx algebraically: Ex.8 (p.75), #10-15

12. Calc 2 HW 1 Candidates: Ch.2.1 # 2, 4, 6, 10, 17, 18
Ch.2.2 # 2, 4, 16, 18, 20, 22 (sketch first!), 30, 36
Ch.2.3 # 6, 8, 10, 12, 14, 23, 27, 33
Due next Thus.11.Nov.04
TA Brian Orr is ill, and will not be in homeroom Wed, but will try to be in QRC at his usual times.
Joey Fedrow is also available – see Help page.