“concavity”的概念、定义、习题解题方法及翻译-数学辞典

单词

concavity

释义

concavity

(concave up and down) A real-valued function f is concave up (or convex) if the chord between any two points (a, f(a)) and (b, f(b)) on the graph y = f(x) always lies above the graph. If the second derivative f″(x) exists and is positive, then f is concave up. The graph of a concave up function lies above any tangent line to the graph. A function is said to be concave up at a value a if it is concave up on some neighbourhood of a.

f is concave down (or just concave) if the chord between any two points (a, f(a)) and (b, f(b)) on the graph y = f(x) always lies below the graph. If f″(x) < 0 for all x, then f is concave down. The graph of f lies entirely below any of its tangents. A function is said to be concave down at a if it is concave down on some neighbourhood of a.

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数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。