Finding Stationary Points of Natural Log Function f(x) = x - 2 ln(x^2 + 3) I started by using the chain rule on x^2+3 which gives me (2x)/(x^2)+3. At this point I tried to multiple (2x)/(x^2)+3 by x−2 - is this correct? How can I then find the stationary point?

anraszbx

anraszbx

Answered question

2022-11-03

Finding Stationary Points of Natural Log Function
f ( x ) = x 2 ln ( x 2 + 3 )
I started by using the chain rule on x 2 + 3 which gives me 2 x x 2 + 3
At this point I tried to multiple 2 x x 2 + 3 by x 2 - is this correct? How can I then find the stationary point?
I understand that you may not wish to give me the answer on a silver platter. Perhaps somebody could kindly provide me with an example in a similar format and the steps involved in solving it.

Answer & Explanation

reinleikcyo

reinleikcyo

Beginner2022-11-04Added 11 answers

The first derivative of your function can be found like this:
f ( x ) = d ( x 2 ln ( x 2 + 3 ) ) / d x = d ( x ) / d x d ( 2 ln ( x 2 + 3 ) ) / d x = 1 2 d ( x 2 + 3 ) / d x x 2 + 3 = 1 4 x x 2 + 3
And the stationary points can be found by solving f ( x ) = 0:
1 4 x x 2 + 3 = 0 4 x x 2 + 3 = 1 x 2 + 3 = 4 x x 2 4 x + 3 = 0 ( x 1 ) ( x 3 ) = 0
So you have x = 1 and x = 3

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