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弧 定义

ARC an abbreviation of average rate of change is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value (Δy) divided by the change in the x-value (Δx) for two distinct points on the graph. It should be noted that average rate of change is not the same thing as the slope of the secant line of a curve. There are several formulas that can be used to calculate average rate of change. They include: average rate of change = ^Δy⁄_Δx = ^{y₂ - y₁}⁄_{x2 - x1} = ^{f(x₂) – f(x₁)}⁄_{x2 - x1} = ^{f(x + h) – f(x)}⁄_h.

给定在 笛卡尔平面 中绘制为 y = f(x) 的函数 f(x)，f 从 x 到 a 的平均变化率（或平均变化率函数）由下式给出: A(x, a) = ^{f(x) - f(a)}⁄_{x - a}。这对应于连接点 (x, f(x)) 和 (a, f(a)) 的割线的斜率。极限值 f'(x) = lim_a->x ^{f(x) – f(a)}⁄_{x - a} 为a 接近 x 的点给出了 切线 在每个点 x 处 f(x) 的 瞬时斜率，这是一个称为 导数，表示为 f'(x) 或 df / dx。