Inequality $\arctan x ≥ x-x^3/3$ Can you help me prove $\arctan x ≥ x-x^3/3$? I have thought of taylor but I have not come up with a solution.

let $$f(x)=\arctan(x)-x+\frac{x^3}{3}$$ for $x\geq 0$ for $x=0$ we get $f(0)=0$ and for $x>0$ we get $$f'(x)=\frac{x^4}{1+x^2}>0$$ therefore we obtain $$f(x)\geq 0$$ for all real $x$ with $x\geq 0$.
