Question

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?
amperes

Answer 1

To find the current \(x\) that produces maximum power in the function \(P(x) = -12x^2 + 120x\), we need to determine the vertex of the parabola represented by this quadratic equation. The standard form of a quadratic function is given by:

\[
P(x) = ax^2 + bx + c
\]

In this case:
- \(a = -12\)
- \(b = 120\)

The x-coordinate of the vertex can be found using the formula:

\[
x = -\frac{b}{2a}
\]

Substituting in the values of \(a\) and \(b\):

\[
x = -\frac{120}{2 \cdot -12} = -\frac{120}{-24} = 5
\]

Thus, the current that will produce the maximum power is

\[
\boxed{5} \text{ amperes}.
\]