Editing Derivative test (section)

===Concavity test===
A related but distinct use of second derivatives is to determine whether a function is [[Concave function|concave up]] or concave down at a point. It does not, however, provide information about [[inflection points]]. Specifically, a twice-differentiable function ''f'' is concave up if <math>f''(x) > 0</math> and concave down if <math>f''(x) < 0</math>. Note that if <math>f(x) = x^4</math>, then <math>x = 0</math> has zero second derivative, yet is not an inflection point, so the second derivative alone does not give enough information to determine whether a given point is an inflection point.