Question

Find the second derivative and it's critical points of f(x)= x/x^2+2

Answer 1

The critical point is where the derivative of f(x)=0 so u need to differentiate once to solve the second part and twice for the first part of ur question. Are u familiar with differenitating a polynominal?

Answer 2

Yeah I did the first derivative but then when I did the 2nd it got alittle messy

Answer 3

Is f(x)=x/(x^2+2) or =x/x^2 +2? It will get messy if it is the later.

Answer 4

It's x/x^2 +2

Answer 5

Then u can simplify 1st be4 differenitate - what would be the simplified form?

Answer 6

1/x+2?

Answer 7

That is correct - so now it should be easier to differeniate ;)

Answer 8

Hmm okay let me see what I get

Answer 9

Post back if u run into any trouble or need more help :)

Answer 10

Okay so I took the derivative and got -x+2/(x+2)^2 idk if that's right

Answer 11

first derivative should be much simplier than that - plz try again or refer to ur book?

Answer 12

f(x)=1/x+2....so what is d/dx(1/x) + d/dx(2)?

Answer 13

Hmm wouldn't i do a quotient rule?

Answer 14

Qutient rule to perform d/dx(1/x) and addition rule for d/dx(A+B)= dA/dx + dB/dx

Answer 15

Wait , omg I just realized I wrote down the wrong problem it's x/(x^2+2) >.< sorry

Answer 16

:( yup then ur life just got a bit more messy now >+<

Answer 17

Ah man I know :/ no wonder I was so confused lol

Answer 18

OK so quotient rule indeed: d/dx(u/v) = (vdu/dx-udv/dx)/dx...
It will be quite long....oh let me see if u got it already....hold on....

Answer 19

f'(x) should be equal to (-x^2+2)/(x^2+2)^2 plz see if u get the same thing :)

Answer 20

Okay I get (-x^2 +2/)(x^2+2)^2^-^

Answer 21

So the critical points for the numerator will be positive and negative square root of 2 ?

Answer 22

yup yup n thats answer to the 2nd part of ur Q...first part: more differentiation :(

Answer 23

Okay so for the second part of when I find f ''(x) can I make it (x^2+2) ( x^2 -2) ^ -2 and do the product rule. ?

Answer 24

Nope quotient rule again because u are missing a "/" there...its a pain but let me know if u wanna try it ;)