Concavity relates to the rate of change of a function’s derivative. A function f is concave up (or upwards) where the derivative f′ is increasing. This is equivalent to the derivative of f′ , which is f′′f, start superscript, prime, prime, end superscript, being positive.

What is a concave up and down?

A function is concave up when it bends up, and concave down when it bends down. The inflection point is where it switches between concavity.

Does concave up mean acceleration is positive?

A concave up position versus time graph has positive acceleration. The reason can be seen by considering the case of a system with constant positive acceleration. The position versus time graph for such a system will be an upward-opening parabola like that shown below.