anonymous
  • anonymous
Where is this function concave up and concave down. x^2/(x-5)^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
klimenkov
  • klimenkov
\[\frac{x^2}{(x-5)^2}\]Can you take derivatives?
anonymous
  • anonymous
yes. I know i have to take the second derivative, but i having trouble finding out where the 2nd derivative equals zero.
anonymous
  • anonymous
I even put the function into a graphing calculator. i still cant get the right answer.

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klimenkov
  • klimenkov
Can you type here what you've got?
anonymous
  • anonymous
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
klimenkov
  • klimenkov
Ok. I will type an answer for you.
anonymous
  • anonymous
this was a multiple part question, this is what i have so far. http://gyazo.com/003eb77ccf9977811aa71cf7f65fb35f
anonymous
  • anonymous
all those answers are right. just need 7 and 8
klimenkov
  • klimenkov
\(f''(x)=\frac2{(-5 + x)^2} - \frac{8 x}{(-5 + x)^3} + \frac{6 x^2}{(-5 + x)^4}\) The horizontal asymtote isn't right.
klimenkov
  • klimenkov
Oh. Sorry. I must check it again!
klimenkov
  • klimenkov
Sorry, I'm not very good in English. Am I right?|dw:1351890529218:dw|
anonymous
  • anonymous
left is concave downward, right is concave up. so you have it backwards
anonymous
  • anonymous
|dw:1351890663750:dw|
klimenkov
  • klimenkov
Ok. So when \(x\in(-\infty,-\frac52)\) it is concave downward. \(x\in(-\frac52,5)\bigcup(5,+\infty)\) it is concave upward.
klimenkov
  • klimenkov
I can solve it right here if you want. It will be not so long.
anonymous
  • anonymous
your right. no need to go any further. :P
klimenkov
  • klimenkov
All you have to do is to solve this:\[\frac2{(-5 + x)^2} - \frac{8 x}{(-5 + x)^3} + \frac{6 x^2}{(-5 + x)^4}=0\]
anonymous
  • anonymous
ye, i was having a tough time with that. :l
anonymous
  • anonymous
hmm. while your here. could you answer 1 small part to another question? pretty straight forward this time
klimenkov
  • klimenkov
Ok, ask anything you like.
anonymous
  • anonymous
http://gyazo.com/3d89eca12903c12ca28e608233e9f102 find critical points
klimenkov
  • klimenkov
Hate this congratulations :)
anonymous
  • anonymous
:o?
anonymous
  • anonymous
people told me there are not critical points to that function, but im not entirely sure if their correct.
klimenkov
  • klimenkov
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?
anonymous
  • anonymous
3, and -3
klimenkov
  • klimenkov
Yes, they are critical.
anonymous
  • anonymous
and 0
anonymous
  • anonymous
but my site says 3, -3 and 0 are not critical points http://gyazo.com/77d0af7eb8d1e3ce273ff32c24eb58ca
klimenkov
  • klimenkov
Are you sure that 0 is a critical point?
anonymous
  • anonymous
your right, its not. f'(0) does not equal 0
anonymous
  • anonymous
but it wont even accept -3 or 3
anonymous
  • anonymous
ugh. wait. i think f'(0)= 0. so it must be a critical point
klimenkov
  • klimenkov
No. It is not right. The derivative is:\[\frac{-4 ( x^2+9 )}{( x^2-9 )^2}\]
anonymous
  • anonymous
oh. so what do you do from there. set it equal to zero and solve? that would be -3 and 3 right?
klimenkov
  • klimenkov
In points -3 and 3 it doesn't exist, so both of them are critical.
anonymous
  • anonymous
ok so that is the answer?
klimenkov
  • klimenkov
Yes. What is the definition of the critical point on your site?
anonymous
  • anonymous
http://gyazo.com/a531cae84cdcc8b853ca750f1e2b5e0c
anonymous
  • anonymous
im not entirely sure. '_'
klimenkov
  • klimenkov
Try to type -3,3 insted of 3,-3
anonymous
  • anonymous
http://gyazo.com/0354e3dc53f2b3172ff9cbbfd156f2a1
anonymous
  • anonymous
this is the problem im having. it wont accept anything.
klimenkov
  • klimenkov
Hm..did you type None into this field?
anonymous
  • anonymous
omg. that actually worked
klimenkov
  • klimenkov
None?
anonymous
  • anonymous
yes. Thanks a lot for the help =]
anonymous
  • anonymous
i did a combined total of 180 tries on both of the question i asked you. finally got the right answers.
klimenkov
  • klimenkov
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.

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