$\"\"$

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The function is $\"\"$ and the interval is $\"\"$ .

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Average rate of change of the function is $\"\"$ .

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Find the average rate of change in the interval $\"\"$ .

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$\"\"$

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The average rate of change in the interval $\"\"$ is $\"\"$ .

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$\"\"$

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Find the instantaneous rate of change in the interval $\"\"$ .

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Instantaneous rate of change is the derivative of the function.

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Instantaneous rate of change at $\"\"$ is $\"\"$ .

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Instantaneous rate of change at $\"\"$ is $\"\"$ .

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Instantaneous rate of change in the interval $\"\"$ is $\"\"$ .

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Hence the average rate of change and the average instantaneous rates are approximately equal.

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$\"\"$

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The average rate of change in the interval $\"\"$ is $\"\"$ .

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Instantaneous rate of change $\"\"$ is $\"\"$ .

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Instantaneous rate of change $\"\"$ is $\"\"$ .