Thread: Find intervals of f increasing/decreasing

1. The problem statement, all variables and given/known data

(a) Find the intervals on which f is increasing or decreasing.
(b) Find the local maximum and minimum values of f.
(c) Find the intervals of concavity and the inflection points.

x2/(x2+3)

2. The attempt at a solution

a) I find that
f'(x)=6x/(x2+3)2

I am stuck because (x2+3)2 has no solutions and I don't know how to define x in order to proceed further.
If anybody can help me out understanding this, I will be very thankful.

Originally Posted by phillyolly

1. The problem statement, all variables and given/known data

(a) Find the intervals on which f is increasing or decreasing.
(b) Find the local maximum and minimum values of f.
(c) Find the intervals of concavity and the inflection points.

x2/(x2+3)

2. The attempt at a solution

a) I find that
f'(x)=6x/(x2+3)2

I am stuck because (x2+3)2 has no solutions and I don't know how to define x in order to proceed further.
If anybody can help me out understanding this, I will be very thankful.

like you said.

Set

So

and so on..

Hi!

How can I solve (x^2+3)^2?
I cannot put x^2+3=0 because x^2=-3 does not exist.

Originally Posted by phillyolly

Hi!

How can I solve (x^2+3)^2?
I cannot put x^2+3=0 because x^2=-3 does not exist.

Why are you trying to solve ? Suppose we have two real numbers and , then .