$\"\"$

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Annual inventory cost for a manufacturer $\"\"$ , where $\"\"$ is the order size.

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Find the rate of change in annual cost when $\"\"$ is increased from $\"\"$ to $\"\"$ .

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Rate of change in annual cost : $\"\"$ .

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$\"\"$

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Rate of change in annual cost when $\"\"$ is increased from $\"\"$ to $\"\"$ is $\"\"$ .

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$\"\"$

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Find the instantaneous rate of change in annual cost when $\"\"$ .

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Instantaneous rate of change in derivative of the function.

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Annual inventory cost : $\"\"$ .

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

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$\"\"$

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Substitute $\"\"$ in the above function.

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$\"\"$

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Instantaneous rate of change in annual cost when $\"\"$ is $\"\"$ .

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Hence change in annual cost when $\"\"$ is increased from $\"\"$ to $\"\"$ is approximately equal to Instantaneous rate of change in annual cost at $\"\"$ .

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$\"\"$

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Rate of change in annual cost when $\"\"$ is increased from $\"\"$ to $\"\"$ is $\"\"$ .

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Instantaneous rate of change in annual cost when $\"\"$ is $\"\"$ .

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Change in annual cost is approximately equal to Instantaneous rate of change in annual cost.