Suppose that f(x)=ln(3+x^2). Use interval notation to state when f(x) is concave up and concave down. Then find all inflection points for f(x).

Answer 1

f' = 2x/(3+x^2)
f" = 2(3-x^2)/(3+x^2)^2

inflection where f" = 0. That is, where

x^2 = 3

concave up where f" > 0