Calculus: Optimization Problem?

Question

Maximizing Power Output of a battery

Formula is: P= VI - RI^2

V= Force in Volts R= Resistance I=Current

V=12 R=0.5

Answer 1

So you want to maximise 12I - 0.5I^2?
Differentiate to get 12 - I = 0, so I = 12.

So power = 12*12 - 0.5*12^2 = 72W.

Answer 2

so P = -0.5 I ^2 + 12 I
this is a downward face parabola. the max occurs when
I = -12 / -1 = 12
if I = 12, then P = 72