2. Objectives Determine tangent lines to functions for a given point Compute the slope of curves Compute Instantaneous rate of change

3. Recall – Average Rate of Change

10. Definition – Secant Line A line through two points on a curve is a SECANT to the curve.

11. Slope of Secant Line

19. You Try

26. Observation What’s the association between average rate of change and the slope of the tangent line?

27. Flies/Day

28. Defn – Tangent Lines A line that intersects a function at exactly one point over a given interval.

29. How to find the slope of the tangent for a curve

32. Example – Slope of a tangent line

36. Secant Slope Calculation

37. Example – Slope of a tangent line

39. Important procedure

40. HW #8, Compute the slope of the secant lines and arrange them in ascending order. What are the appropriate units? 9 – 12 only (a) for these