2. Slope and Equation of a line How to find the slop of a line? (x 1, y 1 ) (x 2, y 2 ) How to find the equation of a line? Sec 2.1: Rates of Change and Tangents to Curves

3. The word tangent is derived from the Latin word tangens, which means “touching.” Tangent line Secant line a line joining two points of a curve is a secant to the curve. slope of a curve at a point P on the curve? the slope of the tangent at P. What is the difference ?? Lines?? Sec 2.1: Rates of Change and Tangents to Curves

4. Is it possible that a line could be tangent and secant in the same time Sec 2.1: Rates of Change and Tangents to Curves

5. Secant line and Tangent line How to find the slope of these lines ?? Tangent line Sec 2.1: Rates of Change and Tangents to Curves

6. Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

7. Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

8. Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

9. Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

10. Secant line and Tangent line Sec 2.1: Rates of Change and Tangents to Curves

11. 1 1 1.2 1.44 Q tangent line Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves 1.25 2.25

12. 1 1 1.2 1.44 Q tangent line Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves 1.25 2.25

13. 1.5(1.5,2.25)2.5 1.2(1.2,1.44)2.2 1.1(1.2,1.21)2.1 1.01(1.01,1.0201)2.01 Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

14. 1 1 x X^2 Example : Find the slope of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

15. 23 1.52.5 1.1 2.1 1.012.01 1.0012.001 1.02.0 tangent line secant line Slope of the tangent line = 2.0 Sec 2.1: Rates of Change and Tangents to Curves

16. 10 1.50.5 1.90.9 1.990.99 1.9990.999 1.02.0 tangent line secant line Equation of the tangent line Slope = 2.0 point = (1, 1) Example : Find the equation of the tangent line to the prabola at the point Sec 2.1: Rates of Change and Tangents to Curves

17. 10 1.50.5 1.90.9 1.990.99 1.9990.999 1.02.0 tangent line secant line Sec 2.1: Rates of Change and Tangents to Curves

18. as means Sec 2.1: Rates of Change and Tangents to Curves

20. EXAM-1 TERM-081

21. Average Speed Instantaneous Speed Average Rates of Change Instantaneous Rates of Change The Derivative as a Rate of Change 3.4 Sec 2.1: Rates of Change and Tangents to Curves Q(2.1):Rates of Change and Tangents to Curves Start: September 2, 2013 11:30 AM End: September 7, 2013 11:30 PM