Average Rate of Change (VCE SSCE Mathematical Methods): Flashcards

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Average Rate of Change
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Formula for average speed

total distance ÷ total time

Average speed on distance-time graph equals

gradient of secant line between two points

Definition of a secant

A line passing through two points on a curve

Definition of a chord

A line segment joining two points on a curve

Average rate of change formula for f(x)f(x) on [a,b][a,b]

f(b)f(a)ba\frac{f(b) - f(a)}{b - a}

Average rate of change geometrically equals

gradient of secant line through (a,f(a))(a, f(a)) and (b,f(b))(b, f(b))

Numerator in average rate of change formula represents

change in yy values

Denominator in average rate of change formula

change in xx values

Average rate of change conceptually is

change in output ÷ change in input

Negative average rate of change indicates

function is decreasing

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