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弧 定義

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.

給定在 笛卡爾平面 中繪製為 y = f(x) 的函數 f(x)，f 從 x 到 a 的平均變化率（或平均變化率函數）由下式給出: A(x, a) = ^{f(x) - f(a)}⁄_{x - a}。這對應於連接點 (x, f(x)) 和 (a, f(a)) 的割線的斜率。極限值 f'(x) = lim_a->x ^{f(x) – f(a)}⁄_{x - a} 為a 接近 x 的點給出了 切線 在每個點 x 處 f(x) 的 瞬時斜率，這是一個稱為 導數，表示為 f'(x) 或 df / dx。