PPT COT 3rd Demo for tangent lines .pptx

tangent lines

1. For 10 seconds, copy exactly what you can read on this slide. This is worth 5 points.

2. How many letter F’s are in this sentence? You have 10 seconds to count them. “FINISHED FILES ARE THE RESULT OF YEARS OF SCIENTIFIC STUDY COMBINED WITH THE EXPERIENCE OF FORTUNATE YEARS.”

3. For 10 seconds, copy exactly what you can read on this slide. This is worth 5 points.

4. This time let us watch a video presentation about how can a single line affects our perspective.

5. Tangent Lines

6. Given a function y=f(x), how do we find the equation of the tangent line at a point? Consider the graph of a function y = f(x) whose graph is given below. Let P(x , y ) be a point on the graph of y = f(x). Our objective is to find the equation of the tangent line (TL) to the graph at the point P(x , y ).

7. Since the tangent line is the limiting position of the secant lines as Q approaches P, it follows that the slope of the tangent line (TL) at the point P is the limit of the slopes of the secant lines PQ as x approaches x . In symbols,  

8. Finally, since the tangent line passes through P(x , y ), then its equation is given by: )  

9. EXAMPLE 1 : Find the equation of the tangent line to y = x 2 at x=2.

10. Example 2. Find the slope-intercept form of the tangent line to

11. Determine the Equation of the tangent line at the curve: Group 1: y = x 2 − 5x + 2 at (3,-4). Group 2: y = x 2 + 3x − 1 at x = 0. Group 3: y = x 2 − 2 at x = 0. Group 4: y = 2x 2 – 4x + 5 at x = -1 Group 5: y = 3x 2 – 12x + 1 at x = 0

12. Evaluation Determine the Equation of the tangent line at the curve:  

13. Homework Determine the Equation of the tangent line at the curve: Show that the tangent line to y = 3x 2 - 12x + 1 at the point (2,-11) is horizontal. Verify that the tangent line to the line y = 2x + 3 at (1, 5) is the line itself.  

14. TEAM QUIZ

15. 1. Determine the Equation of the tangent line at the curve: y = x 2 + 3x − 1 at x = 1

16. Answer y = 5x − 2

17. 2. Determine the Equation of the tangent line at the curve: y = x 2 − 2 at x = -2

18. Answer y = -4x – 6

19. 3. Determine the Equation of the tangent line at the curve: y = 2x 2 – 4x + 5 at x = 0

20. Answer y = -4x + 5

21. 4. Determine the Equation of the tangent line at the curve: y = 3x 2 – 12x + 1 at x = 1

22. Answer y = -6x – 2

23. 5. Determine the Equation of the tangent line at the curve: f(x) = 2x 2 – 3x at x = 0

24. Answer y = -3x

25. 6. Determine the Equation of the tangent line at the curve:  

26. Answer y = + 3  

27. 7. Determine the Equation of the tangent line at the curve:  

28. Answer y = +  

29. 8. Determine the Equation of the tangent line at the curve:  

30. Answer y =  

31. 9. Determine the Equation of the tangent line at the curve:  

32. Answer y = 3

33. 10. Find the point of tangency of the given tangent line to the graph of the function.  

34. Answer P(-3,-21)