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

Given:

The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by:

To find:

The current that will produce the maximum power.

Solution:

We have,

Here, leading coefficient is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a parabola is , then

In the given function, a=-12 and b=120. So,

Putting x=5 in the given function, we get

Therefore, 5 watt current will produce the maximum power of 300 amperes.

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step-by-step explanation: