1. Lab 03 –Labs provide an opportunity to explore, observe, and record a synthesis of your observations. Often the synthesis will include statements from the text or lecture expressed in your own words. The synthesis should always express a deep understanding of the concepts being explored. The Abstract should include this synthesis. –For Lab03, did you discover that the cross section graphs are “side views” and contour graphs are “top down views” of the 3D plot? –Did you discover that the transformation x->x+a shifts the 3D plot along the x- axis, the transformation y->y+a shifts the 3D plot along the y-axis, the transformation f->f+a shifts the 3D plot along the z-axis, the transformation x- >ax stretches/compresses the 3D plot along the x-axis, the transformation y- >ay stretches/compresses the 3D plot along the y-axis, and/or the transformation f->af stretches/compresses the 3D plot along the z-axis? Did you discover that the y-axis cross sections of f(x,y) are stretches/compressions of each other for different values of x?

2. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Section 2.1 Instantaneous Rate of Change Today… We begin Calculus!

3. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Average Rate of Change Average rate of change is a difference quotient. If y = f (x) Instantaneous Rate of Change Compute average rates of change (as difference quotients) over smaller and smaller intervals.

4. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Example: Instantaneous Velocity Average velocity (ft/sec) 8452Instantaneous velocity: in between...

5. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Tabular Exercise Data: Percent of households in the US with cable television as a function of years since Jan. 1, 1990.

6. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Box on page 14 and problem 11 Average Rate of Change Graphically

7. Instantaneous Rate of Change Graphically Compute average rates of change over smaller and smaller intervals.

8. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Graph Exercise

9. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Average Rate of Change Graphically How would you write an expression that represents the slope of a line drawn between the two points marked in Figure 2.5?

10. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Symbolic Exercise

11. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Verbal Exercise

12. Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Handout Start now. Finish for homework.