Question

Inflection points and concavity of these 2 functions:

A.) 4/(1+x^2)

B.) Sin(x/2) in the interval [0,4Pi]

Answer 1

Inflection point by setting Y" to 0 then evaluate the x into my original function and that should be my inflection point(s)
Yet cannot seem to get it right.

Answer 2

F'(x) of 4/(1+x^2) = -8x/(1+x^2)^2
Correct?

Answer 3

The F" of 4/(1+x^2) = -8+24x^2/(1+x^2)3
Correct?

Answer 4

So the result of that set to 0 is equal to -1/SQROOT(3) and 1/SQROOT(3)
Correct???

Answer 5

\[\frac{ 4 }{ 1+x ^{2} } = \frac{ 4 }{ 1+(\frac{ 1 }{ \sqrt{3} }) } \]

Answer 6

the \[(\frac{ 1 }{ \sqrt{3} })^{2}\] Should have looked like that

Answer 7

Should equal positive 3 in both cases so is my Inflection point:
\[(\frac{ 1 }{\sqrt{3} } , 3) \] and \[(-\frac{ 1 }{ \sqrt{3} }, 3)\] or is it just one of those?

Answer 8

It is both does the answer come out wrong?

Answer 9

Not sure it was a hand giving problem to study with, wondering for my own sake if it is correct or not and out of 161 people here only 1 response.
Thank you