y = log(x) is concave down | on x<0 concave down | on x>0

| | concave up | concave down

(no critical points)

d/dx(log(x)) = 1/x

(no critical points)

d^2/dx^2(log(x)) = -1/x^2

{x element R : x>0} (all positive real numbers)

x = 0 (infinite discontinuity) (assuming a function from reals to reals)

abs(x)/(x^2 + 1)^(3/2)

center | (2 x_0 + 1/x_0, -x_0^2 + log(x_0) - 1) radius | (x_0^2 + 1)^(3/2)/abs(x_0) equation | (x - 1/x_0 - 2 x_0)^2 + (1 + y - log(x_0) + x_0^2)^2 = (1 + x_0^2)^3/abs(x_0)^2