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## anonymous one year ago Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2.

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1. anonymous

@dan815 could you help me?

2. anonymous

the derivative formula that I got is f'(x)= -6x+1

3. anonymous

but none of the answers match my answer

4. anonymous

Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2. y = –2x + 2 y = –x + 12 y = –x + 2 y = –2x – 12

5. dan815

|dw:1436827395674:dw|

6. dan815

|dw:1436827520119:dw|

7. dan815

y = –x + 12

8. anonymous

is it 26

9. anonymous

could you explain me how you got that answer

10. anonymous

@dan815

11. dan815

did you get the derivative function right

12. anonymous

yes, because when I plug the value of 2 into my formula I get -1, which you presented me that it was correct, but I don't know how you got that formula

13. dan815

f'(x)= -6x+1 you said you got this, something wrong there

14. dan815

you have to differentiate term by term

15. anonymous

never mind I got -2x+3

16. dan815

okay

17. dan815

now you have a slope, then you find a point that belongs on this tangent line

18. anonymous

but that doesn't have anything in common to the other answers

19. anonymous

how?

20. dan815

|dw:1436828112090:dw|

21. dan815

we know the x coordinate of the point,

22. dan815

now we find the y coordinate of the point and its part of the parabola so

23. dan815

y(2) = ?

24. dan815

|dw:1436828189830:dw|

25. anonymous

do we plug it into the original formula or the derivate one?

26. dan815

we have the slope there, now we need to find the y coordinate then you will have a point and a slope and you figure out the equation of the line

27. dan815

the derivative formula only tells you the slope at every x value

28. dan815

we want to know the actual y point

29. anonymous

so which formula could I use to find the y value?

30. dan815

think about it

31. dan815

the tangent line intersects one point on the parabola, at x=2 and y is something, we can always find the y value for every x value on a parabola how?

32. anonymous

maximum

33. anonymous

wait no, OMG I feel so ignorant.

34. dan815

y = –x^2 + 3x + 8 this equation of parabola

35. dan815

it gives you a y value for every x value

36. dan815

we know there is an intersection at x=2 so we have to see the y value there

37. dan815

y = –x^2 + 3x + 8 y=-2^2+3*2+8 = 10

38. dan815

x=2,y=10 (2,10)|dw:1436828495281:dw|

39. anonymous

I got 10

40. anonymous

yes,

41. dan815

now u have a point at the slope of the tangent line through that point

42. dan815

can you solve the equation of the line from here

43. dan815

y=mx+b m=-1 lets plug in our point to see what b or the y intercept must be 10=-1*2+b b=

44. anonymous

9

45. dan815

10=-1*2+b 10=-2+b b=10+2=12

46. anonymous

Oh i see I thought it was a 1 to the second power

47. dan815

this is the equation of a line y=mx+b

48. anonymous

yeah, OMG I got it. Thank you so much. Could you help me with one more and thats it?

49. dan815

yeah sure

50. anonymous

51. anonymous

I already found that C actually has the value, but I don't know how to solve A nor B

52. anonymous

@dan815

53. anonymous

@phi

54. dan815

|dw:1436829534343:dw|

55. dan815

this is the definition of a derivative

56. dan815

it is the equation to find the slope of a tangent line at x

57. dan815

it arises from taking a secant line where the points are getting closer and closer, lim h--->0

58. dan815

for example take a look at any function f(x)

59. dan815

|dw:1436829711928:dw|

60. dan815

suppose you want to find the derivative at that point x for this function, you can begin to approximate by taking points close to that value because that is a close linear approximation

61. dan815

|dw:1436829768720:dw|

62. anonymous

okay, I see. I got 7 as the slope of the function

63. anonymous

at x=2

64. dan815

|dw:1436829791039:dw|

65. dan815

if we keep making h smaller and smaller then the point is close and closer to the actual tangent slope

66. anonymous

which is 7 right?

67. dan815

|dw:1436829918175:dw|

68. dan815

well my work is done as long you understand how a derivative comes

69. dan815

its from this very simple concept, the slope of the tangent line at some point

70. anonymous

okay than you, I understood the secant and tangent line more.

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