## startanewww 2 years ago Application of differentiation. Find the equation of the normal to the curve y=(x+2)e^x-3x at the point (0,2).

1. startanewww

dy/dx at (0,2) = 0 i don't know what to do next.

2. mark_o.

@ startanewww what did you get on your derivative at (0,2)?

3. startanewww

isn't it 0?

4. mark_o.

after getting the slope at (0,2) find the normal means perpendicular to the line at (0,2)

5. Yahoo!

1st find the equation of tangent to the curve...

6. mark_o.

slope perpendicular to it is m2= - 1/m1

7. Yahoo!

y-y1 = m(x-x1)

8. startanewww

but the slope I found for dy/dx at (0,2) is zero. What can i do?

9. startanewww

then, the slope of the normal will be -1/0 = infinity how can i find the equation of normal?

10. Yahoo!

Diffrentiate y=(x+2)e^x-3x

11. Yahoo!

u know Product Rule ?

12. Yahoo!

u get slope = -1

13. Yahoo!

SO...Slope of Normal = -1 / m1 = -1/-1 = 1

14. Yahoo!

Nw just write the equation using points (0,2) m = 1 y-y1 = m(x-x1)

15. startanewww

y'=e^x+(x+2)e^x-3 dy/dx at (0,2) = e^0 + (0+2)e^0 - 3 = 0

16. startanewww

am i correct?

17. Yahoo!

y=(x+2)e^x-3x y' = (x+2) *1 + e^x *1 - 3

18. startanewww

differentiating e^x gives e^x right?

19. startanewww

am i correct?

20. mark_o.

lets say y'=0, can you form a line perpendicular to the curve? try it :D

21. mark_o.

first fint an equation of the line tangent to the curve at (0,2)

22. startanewww

(y-2)/(x-0)=0 y=2?

23. startanewww

what about the equation of normal?

24. mark_o.

yes correct :D then ?

25. startanewww

what can i do?

26. startanewww

the slope will be infinity....

27. mark_o.

what is a line perpendicular to line y=2?

28. mark_o.

at (0,2) ?

29. startanewww

will the slope of the normal be infinity ?

30. mark_o.

|dw:1356675309579:dw|

31. startanewww

but -1/0 = infinity?

32. startanewww

x=0 is the line

33. startanewww

i don't know the answer....

34. startanewww

i think you are right

35. mark_o.

ah ok theres no answer in the book? :D

36. startanewww

my classmates said the answer was x=0

37. mark_o.

hmm the line perpendicular to y=2 is the y axis or the vertical line

38. startanewww

ok so the answer should be x=0 only?

39. mark_o.

hmm it can be x=0

40. startanewww

x = 0 to infinity?

41. mark_o.

it could be y= 0 to 2, or 2 to infinity, or y= 0 to negative infinity

42. startanewww

?????? how come

43. startanewww

equation of the normal at (0,2)...? should there be only one answer?

44. mark_o.

because line tangent to the curve is y=2 or the horizontal line, now the line normal to it is the line perpendicular to y=2,, w/c are ________ ?

45. startanewww

vertical lines

46. startanewww

?

47. mark_o.

the vertical line y axis

48. mark_o.

yess correct :D

49. startanewww

so what is the final answer? x=0 ?

50. mark_o.

i would say at point (0,2) it is y= from 0 to 2 vertical line

51. startanewww

ok thanks

52. mark_o.

ok YW,,, good luck now :D