Rates and Differentiation (HSC SSCE Mathematics Advanced): Quizzes

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Rates and differentiation
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What does the first derivative f′(x)f'(x) tell us?

The rate at which the function is changing

What does the second derivative f′′(x)f''(x) tell us?

The rate at which the rate is changing

When is a function increasing over an interval?

When f(a)<f(b)f(a) < f(b) for all a<ba < b

For concave up in an interval, where do chords lie?

Above the curve

For concave down in an interval, where do chords lie?

Below the curve

What does increasing at an increasing rate mean?

Increasing AND concave up

What does decreasing at a decreasing rate mean?

Decreasing AND concave up

What does average rate of change correspond to?

A chord gradient

If f′′(x)>0f''(x) > 0 throughout an interval, what is the concavity?

Concave up

What does increasing at a decreasing rate mean?

Increasing AND concave down

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