In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain …

如果定义在某一区间上的一元实函数f (x)是连续函数，且对这一区间中的任何两点X1、X2，当X1＜X2时，有不等式f (q1X1 + q2x2) ≤q1f ( x1)+q2(fx2)，（其中q1、q2为正 …

2016年5月27日 · When the slope continually decreases, the function is concave downward. Taking the second derivative actually tells us if the slope continually increases or decreases. …

2024年9月26日 · A function f is concave or concave down if the line segment between any two points on the graph of the function lies below or on the graph. The curve is ∩-shape, bowl-like …

2020年12月21日 · Our definition of concave up and concave down is given in terms of when the first derivative is increasing or decreasing. We can apply the results of the previous section …

2017年7月20日 · For consistency and coherence between curve shapes in a $(x,y)$ plane and the shape of the surface of lenses, it is better to relate the terms with the sign of the curvature …

Concavity: We can tell within each locale whether the function is concave down, concave up, or not concave. Curvature: Generalizing the tangent line capability a bit, we can do a pretty good …

What Does Curvature Tell Us? What Does PCA Tell Us?

Curvature and Convexity I Erin Pearse | 1-26-06 1. Introduction For smooth surfaces (at least C2, anyway), understood by generalizing d2 dt2 = d dt 0 to higher dimensions. Three perspectives …

2020年7月15日 · We study fully nonlinear geometric flows that deform strictly -convex hypersurfaces in Euclidean space with pointwise normal speed given by a concave function of …