The formula for the power output P of a battery is P = VI - RI where

Question:

The formula for the power output P of a battery is P = VI - RI² where V is the electromotive force in volts, R is the resistance
in ohms, and I is the current in amperes. Find the current that
corresponds to a maximum value of P in a battery for which
V = 12 volts and R = 0.5 ohm. Assume that a 15-ampere fuse
bounds the output in the interval 0 ≤ I ≤ 15. Could the power
output be increased by replacing the 15-ampere fuse with a
20-ampere fuse? Explain.

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