1. Section 2.6 Tangents, Velocities and Other Rates of Change AP Calculus September 18, 2009 Berkley High School, D2B2

2. Calculus, Section 2.62 Slope of the tangent line Definition 1: The tangent line to the curve y=f(x) at the point P(a,f(a)) is the line through P with the slope…

3. Calculus, Section 2.63

4. 4 Example Find an equation of the tangent line to the parabola y=x 2 at the point P(1,1)

5. Calculus, Section 2.65 Example Find an equation of the tangent line to the parabola y=x 2 at the point P(1,1)

6. Calculus, Section 2.66 Slope of the tangent line Definition 2: The tangent line to the curve y=f(x) at the point P(a,f(a)) is the line through P with the slope…

7. Calculus, Section 2.67

8. 8 Example Find an equation of the tangent line to the hyperbola y=3/x at the point P(3,1).

9. Calculus, Section 2.69 Example Find an equation of the tangent line to the hyperbola y=3/x at the point P(3,1).

10. Calculus, Section 2.610 Velocity As we discussed earlier, if the equation describes position, then the slope represents velocity. The secant line (between two points on the curve) represents average velocity. The tangent line represent instantaneous velocity.

11. Calculus, Section 2.611 Velocity The tangent line represent instanteous velocity.

12. Calculus, Section 2.612 In general… The secant line (between two points on the curve) represents average rate of change. The tangent line represent instantaneous rate of change. Look at what they are asking for in the problems, and use the appropriate definition.

13. Calculus, Section 2.613 Assignment Section 2.6, 1-17, odd (exclude 5)

14. Calculus, Section 2.614

15. Calculus, Section 2.615

16. Calculus, Section 2.616

17. Calculus, Section 2.617