# Is f(x) =(x-2)^3/(x^2/3+1) concave or convex at x=6?

To know if a function is concave or convex we use the second derivate, we substitute by one point and if the number we get it's negative the function is concave, if it's positive means that it's convex and if it's $0$ means that it's an inflection point.
$f ' ' \left(x\right) = \frac{54 {x}^{3} + 180 {x}^{2} - 486 x - 180}{{\left({x}^{2} + 3\right)}^{3}}$
$f ' ' \left(6\right) = \frac{1672}{6591} \cong 0.2537$