What is the maximum power and corresponding current for a car battery?

[chawki]

Homework Statement

The voItage U of a car battery decreaces as a function of the current I according to
the formula U(I) = 12-0.3*I
The power P of the starting motor is the product of the current I and voItage U , P(I) = U(I)* I.

Homework Equations

Find the maximum value of the power and the corresponding current. (The units corresponding to the numerical values of the functions are standard units, Thus the units of the voItage, current and power are V, A and W)

The Attempt at a Solution

P=(12-0.3*I)*I
P=12I-0.3I²
P' =-0.6I+12

P'=0
-0.6I=-12
I=20 Amperes

P=(12-0.3*20)*20
P=120 Watt

 

[Delphi51]

That looks good, chawki.