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9.01 Average and instantaneous rates of change

Interactive practice questions

A bucket containing water has a hole through which the water leaks. The graph shows the amount of water remaining in the bucket after a certain number of minutes.

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a

What is the slope of the line?

b

What does the slope tell you?

The amount of water in the bucket increases by $1$1 litre every $\frac{1}{2}$12 minute.

A

The amount of water in the bucket decreases by $\frac{1}{2}$12 litre every minute.

B

The amount of water in the bucket decreases by $1$1 litre every $\frac{1}{2}$12 minute.

C

The amount of water in the bucket increases by $\frac{1}{2}$12 litre every minute.

D
Easy
3min

The graph shows the cost, in dollars, of a phone call for different call durations.

Easy
2min

The table shows Skye's progress through a four-hour ultramarathon.

Easy
3min

The table shows the linear relationship between the temperature on a particular day and the net profit of a store. Find the rate of change of net profit.

Easy
2min
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Outcomes

2.3.1

interpret the difference quotient [f(x+h)−f(x)]/h as the average rate of change of a function f

2.3.4

interpret the ratios [f(x+h)−f(x)]/h and δy/δx as the slope or gradient of a chord or secant of the graph of y=f(x)

2.3.5

examine the behaviour of the difference quotient [f(x+h)−f(x)] / h as h→0 as an informal introduction to the concept of a limit

2.3.10

estimate numerically the value of a derivative, for simple power functions

2.3.11

examine examples of variable rates of change of non-linear functions

2.3.16

determine instantaneous rates of change

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