The power generated by an electrical circuit (in watts) as a function of its current x (in amperes) is modeled by: P(x)=-12x^2+120x What current will produce the maximum power?

A current of 5 amperes will produce the maximum power.

Step-by-step explanation:

Let be , where is measured in watts and in amperes. At first we must obtain the first and second derivatives of the function to determine the current associated with maximum power. That is:

First derivative

Second derivative

Now, we equalize the first derivative to zero and solve it afterwards: (First Derivative Test)

The only critical point is .

As next step we need to assure that critical point leads to an absolute maximum by evaluating the critical point found above in the second derivative: (Second Derivative Test)

Which indicates that critical point leads to an absolute maximum.

A current of 5 amperes will produce the maximum power.

answer: 2 litters juice bottle

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hope this ^_^