$\"\"$

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The power output function is $\"\"$ .

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Where $\"\"$ is electromotive force $\"\"$ volts.

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$\"\"$ is resistance $\"\"$ ohms.

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So $\"\"$ .

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When $\"\"$ then $\"\"$ .

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When $\"\"$ then $\"\"$ .

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To find the maximum output power , derivative the power function and equate to zero.

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$\"\"$

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Apply derivative with respect to $\"\"$ .

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$\"\"$

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Equate it to zero .

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$\"\"$

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Critical number is $\"\"$ .

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When $\"\"$ then $\"\"$ .

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When $\"\"$ then $\"\"$ .

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So the maximum out power occurs when $\"\"$ .

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$\"\"$

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The maximum out power lies in the interval $\"\"$ ( $\"\"$ amp fuse ).

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The power output will not increase by replacing the $\"\"$ amp fuse with $\"\"$ amp fuse.

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Because the output power decreases for $\"\"$ .

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$\"\"$

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The maximum out power is $\"\"$ .