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## hba 2 years ago Checking my answers if f(x)=x^3-9x^2+15x+3 What is the relative maxima ?

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1. hba

I got 10.

2. waterineyes

Really??

3. hba

Yeah really.

4. waterineyes

It will be right as it is calculated by the Great @hba ha ha ha..

5. hba

Thanks.

6. hba

I have more question to get checked can i ask here or in a new post.

7. waterineyes

I don't know how to solve these types of questions.. Can you teach me how to solve it..??

8. hba

@waterineyes Ha Ha Ha Nice joke,first let me ask my questions.

9. waterineyes

First, we will take derivative.. Right??

10. hba

Yeah.

11. waterineyes

So wait, I am doing it..

12. hba

okay :(

13. waterineyes

f'(x) = 3x^2 - 18x + 15

14. sirm3d

there are two extrema, 1 relative maximum and 1 relative minimum.

15. waterineyes

Should I factorize it??

16. hba

put f'(x)=0

17. waterineyes

Yes I mean the same..

18. hba

Then the answer is yes

19. waterineyes

$x^2 - 6x + 5 = 0 \implies (x - 5)(x - 1) = 0$

20. waterineyes

x = 5 and x = 1

21. hba

Yes you are right

22. hba

Now put 1 in the orignal equation.

23. waterineyes

Why not 5 ??

24. hba

Because we are finding the relative maxima

25. waterineyes

f(1) = 10

26. sirm3d

oooh, i misread the problem. relative maxima.

27. hba

Correct.

28. waterineyes

So, we have to put smaller value??

29. hba

Yes.

30. waterineyes

Just checking your answer.. Ha ha ha..

31. waterineyes

Now don't say, to find relative minima, we will put 5..

32. hba

|dw:1355817149046:dw|

33. hba

@waterineyes Check these two questions.

34. waterineyes

How to solve these now??

35. hba

I got f'(x)=e in both the cases.

36. hba

And f''(x)=1/e for 1st and f''(x)=e in the 2nd one.

37. hba

So i am right ?

38. waterineyes

Are you sure it is e ??

39. hba

Pretty sure Because i did this one like 100 times when i was in High school

40. waterineyes

You have used division rule here??

41. hba

U/V form.

42. waterineyes

For first : $f'(x) = \frac{1 - \ln(x)}{x^2}$

43. hba

Wait lemme check.

44. waterineyes

Take your time..

45. hba

Yeah right

46. hba

@waterineyes ?

47. waterineyes

Who is right??

48. hba

The most intelligent @waterineyes

49. waterineyes

Not intelligent as you @hba

50. waterineyes

Now, find the second derivative..

51. hba

Ha Ha Ha Yeah wait.

52. hba

I am getting something,which looks extremly wrong :/

53. hba

@waterineyes Here you go $f''(x)=-x-2x+2lnx/x^4$ I kow it's wrong :/

54. waterineyes

Sorry busy helping other person..

55. waterineyes

Now I think, if it was e then it will be simpler..

56. waterineyes

Wait, let me check..

57. hba

ok

58. waterineyes

You can add first two terms in the numerator..

59. hba

Yeah i can add them so, $f''(x)=-3x+2lnx/x^2$

60. hba

@waterineyes So ?

61. hba

@waterineyes Ansoo kahan ho tum ?

62. hba

@waterineyes Answer tau sahi hai mera,Is ki working mushkil hai :/

63. waterineyes

Now what to do next??

64. waterineyes

I had a guest in home so busy there.. Sorry, let us now work together..

65. waterineyes

There??

66. hba

yeah

67. hba

@waterineyes Where should i continue ?

68. waterineyes

What we will do next after finding second derivative?? To find extreme value..

69. hba

put it equal to 0

70. waterineyes

$2 \ln(x) = 3x$

71. waterineyes

Where are we going?? Is that right??

72. hba

i think we should skip these lol,I am pretty sure about my answers :) Do you know what is a stationary point ?

73. waterineyes

The point which is stationary is called Stationary Point, that's it..!!!

74. hba

So, if f(x)=ln(1+x^2) What will be the stationary point ?

75. waterineyes

I think I should go now.. Ha ha ha.. Seriously, don't know..

76. hba

Gurpreet :/ Chalo Bye.

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