Find the critical point of x/(x^2 +3)A

how would i find the critical point of x/(x^2 +3)?
first i need to find the derivative is it? 6x/(x^2 +3) ???
if not how would i do it? thanks!

1)

Download Graph 4.4 from www.padowan. dk for free.

On "Axes", change the range of Y edge from - 1 to 1, then "OK".

On "Function I Insert function", type x/(x^2 +3), then "OK".

You'll see the points of max and min.

To find them:

diff(x/(x^2+3), x) = 1/(x^2 + 3) - 2*x^2/(x^2 + 3)^2

solve(1/(x^2+3) - 2*x^2/(x^2+3)^2 = 0)

x1 = - sqrt(3), x2 = sqrt(3)

f(x) = x/(x^2 +3)

f( - sqrt(3)) = - (1/6)*sqrt(3)

point ( - sqrt(3); - (1/6)*sqrt(3)) = Minimum

f(sqrt(3)) = (1/6)*sqrt(3)

point (sqrt(3); (1/6)*sqrt(3)) = Maximum