# Lesson Worksheet: Average and Instantaneous Rates of Change Mathematics • Higher Education

In this worksheet, we will practice finding the average rate of change of a function between two x-values and using limits to find the instantaneous rate of change.

Q1:

Evaluate the average rate of change for the function when changes from 1 to 1.5.

Q2:

A farm’s production in kilograms as a function of the kilograms of insecticide is given by . Find the average rate of change in when varies from 13 to 17.

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Q3:

Determine the average rate of change function for at .

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Q4:

Find the average rate of change function of when .

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Q5:

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

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Q6:

Suppose a population is as a function of time . What is the average rate of growth of this population when changes from to ?

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Q7:

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

Q8:

Evaluate the instantaneous rate of change of at .

Q9:

Find the instantaneous rate of change of at .

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Q10:

The biomass of a bacterial culture in milligrams as a function of time in minutes is given by . What is the instantaneous rate of growth of the culture when ?

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