Inflection Point.....HELP

[nikchic5]

Is this correct?
(x^2) / (x^2 + 9)
is there an inflection point at (sqrt 3,1/4)

Thanks so much!

 

[soroban]

Hello, nikchic5!

\(\displaystyle \Lf(x)\:=\: \frac{x^2}{x^2\,+\,9}\)

Is there an inflection point at \(\displaystyle \left(\sqrt{3},\,\frac{1}{4}\right)\)

Yes, but there are two inflection points . . .

We have: \(\displaystyle \L\:f'(x)\:=\:\frac{18x}{(x^2\,+\,9)^2}\;\) and \(\displaystyle \L\;
f''(x)\;=\;\frac{54(3 - x^2)}{(x^2\,+\,9)^3}\)

So we have: \(\displaystyle \L\,3\,-\,x^2\:=\:0\;\;\Rightarrow\;\;x^2\,=\,3\;\;\Rightarrow\;\;x\,=\,\pm\sqrt{3}\)

 

[nikchic5]

Ok thank you very much...one more question though?
Is there an inflection point on (x^3-1) / (x^3+1) at (-2, 9/7) and (1,0) thanks soo much! You save my life!