Derivative of x^2/(x^2 +3)

derivative of x^2/(x^2 +3)?
and from that how would i find the critical points?

y = x^2/(x^2 +3)
dy/dx = [(x^2 + 3)(2x) - x^2(2x)] / (x^2 + 3)^2
= [(2x)(x^2 + 3 - x^2] / (x^2 + 3)^2
= 6x / (x^2 + 3)^2

Critical points occur where
dy/dx = 0 OR dy/dx DNE
(Don't forget your DNE critical points.)

dy/dx exists for all x, so there are no DNE critical points.
dy/dx = 0
6x / (x^2 + 3)^2 = 0
6x = 0
x = 0

So the critical point occurs at x = 0.

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

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

x = 0

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

f(0) = 0

point (0, 0) = Minimum

If you want to see the graph, download Graph 4.4 from www.padowan.dk for free.

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