Rates and Differentiation (HSC SSCE Mathematics Advanced): Flashcards

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Rates and differentiation
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What f′(x)f'(x) tells us

Rate at which function is changing

What f′′(x)f''(x) tells us

Rate at which the rate is changing

Increasing in interval: f(a)f(a) vs f(b)f(b) when a<ba<b

f(a)<f(b)f(a) < f(b)

Decreasing in interval: f(a)f(a) vs f(b)f(b) when a<ba<b

f(a)>f(b)f(a) > f(b)

Concave up: chord position

Above the curve

Concave down: chord position

Below the curve

Increasing at increasing rate means

Increasing AND concave up

Decreasing at decreasing rate means

Decreasing AND concave up

Average rate of change formula

Q2−Q1t2−t1\frac{Q_2 - Q_1}{t_2 - t_1}

Average rate uses ___, instantaneous rate uses ___

Chord, tangent

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