## IsTim 3 years ago Find the equation of the tangent to the curve at the given x value.

1. IsTim

|dw:1335261368315:dw|

2. IsTim

I got up to this:|dw:1335261401688:dw|

3. IsTim

|dw:1335261446849:dw|

4. chaise

Calculate the derivative of the equation, make the equation to equal, solve it and plug in your x value. Are you familiar with the quotient rule in derivatives?

5. IsTim

Deriatives is f'(x) right? we're not doing that yet.

6. IsTim

Methods we're using is substitution, factoring and the conjugate method.

7. IsTim

I'm using the Calculus Phobe videos from Calculus Help (my teacher showed me the website and told me to use that).

8. chaise

Yes, that's correct. So you're differentiating using the definition? If you take the derivative of the equation y=3/(x^2-1) you can find the slope. if: f(x)=3/(x^2-1) then f(x+h)=3/((x+h)^2-1) dy/dx = (f(x+h)-f(x))/h Can you do the rest?

9. chaise

dy/dx =lim (h-->0) (f(x+h)-f(x))/h rather.

10. IsTim

Yes. That's what I did.

11. IsTim

But I can't go any further. |dw:1335262087563:dw| That's the furthest I got up to.

12. chaise

Expand your brackets and factor out a h.

13. IsTim

The bottom one to? I was told not too.

14. chaise

Not sure - I'm not familiar with the long method, I just use the shortcut :)

15. Callisto

Can you take derivatives? Must you use first principle to find it?

16. IsTim

Derivatives is our next unit.

17. IsTim

I can't isolate or factor out anything. I must had made a mistake beforehand I guess.

18. IsTim

Anyone?

19. Callisto

I hope you don't mind me posting my solution here

20. IsTim

I guess not, but it's notm much like my work.

21. Callisto

Oh shoot... I got some mistakes there! Wait

22. Callisto

Once again :(

23. Callisto

Oh my dear!!! The final answer should be -4/3 ... not -2 as I've written :S

24. Callisto

Is your question $\frac{3}{x^2-1}$ or $\frac{3}{x^2+1}$?

25. IsTim

First one.

26. IsTim

Maybe I should upload my work, and maybe you check for problems?

27. Callisto

Sure!

28. IsTim

IT's c.

29. IsTim

Starting from c) at Scan001.

30. Callisto

f(a) is not 1

31. Callisto

f(a) is 3/ (a^2 -1)

32. IsTim

but since x=2, I subbed in a=2 into that equation...

33. Callisto

for the denominator, (a+h)-a =h , not a+h -2 You need to find the limit before substituting the numbers.

34. Callisto

After you've found the limit, you'll see the unknown x. By then, sub x=2 and you'll get the slope. But NOT when you're taking the limit

35. IsTim

I thought the unknown to be m, and that h was still the variable withint the equation?

36. Callisto

h is something you need to deal with. Should I upload an example to should how you do first principle for you ?

37. IsTim

I've got an example here with me from my teacher.

38. Callisto

If you don't need it, it's okay :) Should I keep checking for you or you want to do corrections first?

39. IsTim

What should I correct?

40. Callisto

Correct starting from the third line For numerator: a -> 3/ (a^2 -1) For denominator: a+h-2 -> h (in your previous step, a+h -a, simplify it , you'll get h)

41. IsTim

Sorry if I sound ignorant, but that's how I saw it in the example...the h is alone.

42. Callisto

43. IsTim

44. Callisto

First, the situation is different . You're given 2 values there, but only 1 here. Second, to be frank, I don't understand what you (or your teacher) is doing. It's not the normal way as I've learnt.. Third, I still insist that you shouldn't sub the value immediately...

45. IsTim

Ok. I think I know what you are doing, and what my teacher is doing. You're going from a general formula, while my teacher is using the specific formula. The general formula doesn't sub in the x or a value until the end.

46. Callisto

It's good that you notice the difference :)

47. IsTim

Just looking through my notes I guess. I've got a test coming up, so I thought reviewing would be best.

48. Callisto

Yup :)

49. Mimi_x3

well, where do you need help with? This is pretty long..

50. IsTim

Maybe I should just leave this question. I tried this for over 2 hours by now.

51. Mimi_x3

First, what is the question? $\frac{1}{x-2}$?? or $\frac{3}{x^{2}-1}$??

52. IsTim

Second one, whereas x=2.

53. IsTim

Ok. Thanks for the attempt guys. I'll try other problems, and maybe this might make more sense.

54. Mimi_x3

wait..i will try and do it first.. can't you take the derivative which is easier?

55. IsTim

Others suggested that, but that's for the next unit. I understand a bit on how that works, but I'm not allowed using it here.

56. Mimi_x3

Hmm..I might try it but it might take a while since i havent done these in a while...

57. IsTim

Ok. Well, I guess you can do so, if yo uhave free time. But most likely you too have something important coming up (immediately).

58. Mimi_x3

No, I don't have anything important..i might be able to do it but not sure..lol

59. Mimi_x3

I have to review these anyway

60. apoorvk

^^That was mammoth. phew. Istim do you know how to differentiate using chain rule?

61. Mimi_x3

lol, i failed...do you remember how to do these apoor? my brain is failling me :(

62. IsTim

No, I don't (Sorry, cleaning up house).

63. apoorvk

Hmm. so you want to do this by the first principle of finding derivatives okay.

64. IsTim

I am just oh so selective in the method used. That be the end of me.

65. Mimi_x3

$\large\frac{f(x+h)-f(x)}{h} =>\frac{\frac{3}{(x+h)^{2}-1}-\frac{3}{x^{2}-1}}{h}$

66. Mimi_x3

right so far?

67. IsTim

I have no idea.

68. chaise

should be the limit as h approaches zero, but, apart from that, correct. ^_^

69. Mimi_x3

$\large =>\frac{\frac{3}{h^{2}+2hx+x^{2}-1}-\frac{3}{x^{2}-1}}{h}$ $\large >\frac{\frac{3(x^{2}-1)-3(h^{2}+2hx+x^{2}-1)}{(h^{2}+2hx+x^{2}-1)(x^{2}-1)}}{h}$

70. Mimi_x3

I think that im doing it wrong..i dont think that its this complicated..

71. chaise

Perhaps you should just use quotient rule.

72. Mimi_x3

but it says derivatiive thing is not allowed..

73. IsTim

Before using deratives. Referencing Calculus Phobe from Calculus Help. I think I used Conjugate Method.

74. Mimi_x3

whaat..im lost..i looked at your example but it got confusing..then i looked at my book its more confusing..using the chain rule is easier.

75. Mimi_x3

$\frac{3}{x^{2}-1} => 3(x^2-1)^{-1}$ $-3(x^2-1)^{-1}*2x$ $-6x(x^2-1)^{-1}$ easier i suppose..