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平均値 定義
Average rate of change or ARC 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.
上記のデカルト平面にy=f(x)としてプロットされた関数f(x)が与えられると、xからaへのfの平均変化率(または平均変化率関数)は次の式で与えられます。 :A(x、a)= f(x)– f(a)⁄ x-a。これは、点(x、f(x))と(a、f(a))を結ぶ割線の傾きに対応します。制限値f'(x)= lim a-> x f(x)– f(a)⁄ x-a as点aがxに近づくと、各点xでf(x)に接線の瞬間勾配が与えられます。これは導関数、f'(x)またはdf/dxで表されます。
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“Average Rate of Change.” From Wolfram MathWorld, mathworld.wolfram.com/AverageRateofChange.html.
“Average Rate of Change.” Mathwords, www.mathwords.com/a/average_rate_change.htm.