## steel11 Group Title Where is this function concave up and concave down. x^2/(x-5)^2 one year ago one year ago

1. klimenkov Group Title

$\frac{x^2}{(x-5)^2}$Can you take derivatives?

2. steel11 Group Title

yes. I know i have to take the second derivative, but i having trouble finding out where the 2nd derivative equals zero.

3. steel11 Group Title

I even put the function into a graphing calculator. i still cant get the right answer.

4. klimenkov Group Title

Can you type here what you've got?

5. steel11 Group Title

going to take me a while to get it, have to do chain rule and everything. '_' you can just post the answer if you want. >.> already been on this problem for like an hour

6. klimenkov Group Title

Ok. I will type an answer for you.

7. steel11 Group Title

this was a multiple part question, this is what i have so far. http://gyazo.com/003eb77ccf9977811aa71cf7f65fb35f

8. steel11 Group Title

all those answers are right. just need 7 and 8

9. klimenkov Group Title

$$f''(x)=\frac2{(-5 + x)^2} - \frac{8 x}{(-5 + x)^3} + \frac{6 x^2}{(-5 + x)^4}$$ The horizontal asymtote isn't right.

10. klimenkov Group Title

Oh. Sorry. I must check it again!

11. klimenkov Group Title

Sorry, I'm not very good in English. Am I right?|dw:1351890529218:dw|

12. steel11 Group Title

left is concave downward, right is concave up. so you have it backwards

13. steel11 Group Title

|dw:1351890663750:dw|

14. klimenkov Group Title

Ok. So when $$x\in(-\infty,-\frac52)$$ it is concave downward. $$x\in(-\frac52,5)\bigcup(5,+\infty)$$ it is concave upward.

15. klimenkov Group Title

I can solve it right here if you want. It will be not so long.

16. steel11 Group Title

your right. no need to go any further. :P

17. klimenkov Group Title

All you have to do is to solve this:$\frac2{(-5 + x)^2} - \frac{8 x}{(-5 + x)^3} + \frac{6 x^2}{(-5 + x)^4}=0$

18. steel11 Group Title

ye, i was having a tough time with that. :l

19. steel11 Group Title

hmm. while your here. could you answer 1 small part to another question? pretty straight forward this time

20. klimenkov Group Title

21. steel11 Group Title

http://gyazo.com/3d89eca12903c12ca28e608233e9f102 find critical points

22. klimenkov Group Title

Hate this congratulations :)

23. steel11 Group Title

:o?

24. steel11 Group Title

people told me there are not critical points to that function, but im not entirely sure if their correct.

25. klimenkov Group Title

The definition of the critical point says that it is that point where the derivative of the function is equal to zero or DOES NOT EXIST. It is your case. Wat are the point where it doesn't exist?

26. steel11 Group Title

3, and -3

27. klimenkov Group Title

Yes, they are critical.

28. steel11 Group Title

and 0

29. steel11 Group Title

but my site says 3, -3 and 0 are not critical points http://gyazo.com/77d0af7eb8d1e3ce273ff32c24eb58ca

30. klimenkov Group Title

Are you sure that 0 is a critical point?

31. steel11 Group Title

your right, its not. f'(0) does not equal 0

32. steel11 Group Title

but it wont even accept -3 or 3

33. steel11 Group Title

ugh. wait. i think f'(0)= 0. so it must be a critical point

34. klimenkov Group Title

No. It is not right. The derivative is:$\frac{-4 ( x^2+9 )}{( x^2-9 )^2}$

35. steel11 Group Title

oh. so what do you do from there. set it equal to zero and solve? that would be -3 and 3 right?

36. klimenkov Group Title

In points -3 and 3 it doesn't exist, so both of them are critical.

37. steel11 Group Title

ok so that is the answer?

38. klimenkov Group Title

Yes. What is the definition of the critical point on your site?

39. steel11 Group Title
40. steel11 Group Title

im not entirely sure. '_'

41. klimenkov Group Title

Try to type -3,3 insted of 3,-3

42. steel11 Group Title
43. steel11 Group Title

this is the problem im having. it wont accept anything.

44. klimenkov Group Title

Hm..did you type None into this field?

45. steel11 Group Title

omg. that actually worked

46. klimenkov Group Title

None?

47. steel11 Group Title

yes. Thanks a lot for the help =]

48. steel11 Group Title

i did a combined total of 180 tries on both of the question i asked you. finally got the right answers.

49. klimenkov Group Title

It is strange. Ask your teacher the definition of the critical point. Hope you will solve different problems easily in the future. Good luck for you. I wish you a lot of well. Hope you understand.