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Cost of producing $\"\"$ units of a certain commodity is $\"\"$

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(a)

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Average rate of change of $\"\"$ with respect to $\"\"$ :

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(i)

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when production level is changed from $\"\"$ to $\"\"$ :

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Cost of producing $\"\"$ units is $\"\"$ .

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$\"\"$

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Cost of producing $\"\"$ units is $\"\"$ .

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$\"\"$

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Average rate of change of $\"\"$ from $\"\"$ to $\"\"$ is $\"\"$

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$\"\"$

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Average rate of change of $\"\"$ from $\"\"$ to $\"\"$ is $\"\"$ dollars/unit.

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(ii)

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When production level is changed from $\"\"$ to $\"\"$ :

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Cost of producing $\"\"$ units in that commodity is $\"\"$ .

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$\"\"$

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Cost of producing $\"\"$ units in that commodity is $\"\"$ .

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$\"\"$

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Average rate of change of $\"\"$ from $\"\"$ to $\"\"$ is $\"\"$

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$\"\"$

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Average rate of change of $\"\"$ from $\"\"$ to $\"\"$ is $\"\"$ dollars/unit.

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(b)

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Instantaneous rate of change of $\"\"$ with respect to $\"\"$ when $\"\"$ :

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The derivative $\"\"$ is the instantaneous rate of change of $\"\"$ with respect to $\"\"$ at $\"\"$ .

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Instantaneous rate of change $\"\"$

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Here $\"\"$ .

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Let $\"\"$

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$\"\"$

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Instantaneous rate of change of $\"\"$ when $\"\"$ is $\"\"$ dollars/unit.

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(a)

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(i) Average rate of change of $\"\"$ from $\"\"$ to $\"\"$ is $\"\"$ dollars/unit.

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(ii) Average rate of change of $\"\"$ from $\"\"$ to $\"\"$ is $\"\"$ dollars/unit.

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(b)

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Instantaneous rate of change of $\"\"$ when $\"\"$ is $\"\"$ dollars/unit.