# Worksheet: Moving from Average Rates of Change to Instantaneous Rates of Change

Q1:

Determine the average rate of change function for when changes from to .

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Q2:

The average rate of change of a function between and is . Compute this quantity for at , and for .

Q3:

If the function , find .

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Q4:

If the function , find .

• A9
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• E

Q5:

If the function , find .

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Q6:

If the function , find .

• A12
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Q7:

If the function , find .

• A28
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• E

Q8:

If the function , find .

• A4
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• E

Q9:

For a function , the average rate of change between a fixed point and another point is . Given that , find when .

Q10:

Find the average rate of change of when varies from 1.3 to 2.

Q11:

Consider the average rate of change of the function over the interval with small values of .

Simplify the expression .

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The average rate of change gets closer and closer to as becomes smaller and smaller. Simplify the expression for the difference between and .

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For what values of is the difference exactly , , . Give your answer as a fraction.

• A , ,
• B , ,
• C27, ,
• D , ,
• E27, ,

Q12:

What is the average rate of change function for the function ?

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