what is the second derivative of 1 over x squared plus 3

Question

Sketch the graph of 1/x^2+3. determine intervals where the function 1/x^2+3 is increasing, decreasing, concave up or down, any relative extrema, all points of inflection, all intercepts and all asymptotes.

Answer 1

Graph of f(x)=1/(x²+3) is below:

There is a maximum at x=0 (the point (0,⅓)), concave down, the only extremum. The function is increasing from x=-∞ to 0, interval (-∞,0]. The x-axis (y=0) is the asymptote. The y-intercept is ⅓. No x-intercept.