Differentiability: Everything You Need To Know
Differentiability and Smoothness: A function is differentiable at a point if it is “smooth” (without sharp corners or cusps) and continuous at that point. The smoothness implies that the function’s graph can be approximated by a tangent line at every point where the function is differentiable. Differentiability and Continuity: While differentiability implies continuity, the converse […]
The Slope of The Slope: Second Derivatives
TL;DR: If the first derivative tells you the slope, the second derivative tells you how that slope is changing. It is the derivative of the derivative. Concavity comes from its sign — positive means the curve bows up, negative means it bows down — and the spots where it flips sign are inflection points. In […]
