📐 平均变化率计算器Average Rate of Change Calculator

使用说明与常见问题How-to & FAQ

「平均变化率计算器」是什么？What is the Average Rate of Change Calculator tool?

求函数 f(x) 在区间 [a, b] 上的平均变化率 (f(b) − f(a)) ÷ (b − a)，即割线斜率；可输入函数表达式，也可直接输入两点的函数值。Find the average rate of change of f(x) over [a, b] — (f(b) − f(a)) ÷ (b − a), the slope of the secant line — from a function expression or directly from two function values.

如何使用「平均变化率计算器」？How do I use the Average Rate of Change Calculator tool?

在「平均变化率计算器」中，填写「输入方式」、「函数 f(x)」、「区间起点 a」、「区间终点 b」、「f(a)」等参数，结果会随输入实时计算并显示在下方。In the Average Rate of Change Calculator: Fill in "Input", "Function f(x)", "Interval start a", "Interval end b", "f(a)"; results are recalculated instantly as you type.

平均变化率怎么算？How is the average rate of change calculated?

平均变化率 = (f(b) − f(a)) ÷ (b − a)，几何上是连接 (a, f(a)) 和 (b, f(b)) 两点的割线斜率。Average rate of change = (f(b) − f(a)) ÷ (b − a) — geometrically, the slope of the secant through (a, f(a)) and (b, f(b)).

函数怎么写？How do I type the function?

支持 + − * / ^、括号、隐式乘法（如 3x）以及 sin、cos、tan、sqrt、ln、log、exp、abs 等函数，常数可用 pi 和 e。三角函数使用弧度。Use + − * / ^, brackets, implicit multiplication such as 3x, and functions like sin, cos, tan, sqrt, ln, log, exp and abs, with constants pi and e. Trig functions use radians.

计算精度如何？How precise are the results?

「平均变化率计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Average Rate of Change Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.

「平均变化率计算器」免费吗？需要注册吗？Is the Average Rate of Change Calculator free? Do I need an account?

「平均变化率计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Average Rate of Change Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.