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NemiM [27]
3 years ago
7

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+1

20x What current will produce the maximum power?

Mathematics
1 answer:
ra1l [238]3 years ago
6 0

Answer:

A current of 5 amperes will produce the maximum power.

Step-by-step explanation:

Let be p(x) = -12\cdot x^{2}+120\cdot x, where p(x) is measured in watts and x 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

p'(x) = -24\cdot x + 120

Second derivative

p''(x) = -24\cdot x

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

-24\cdot x + 120 = 0

x = 5\,A

The only critical point is x = 5\,A.

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)

p(5)'' = -24\cdot (5)

p''(5) = -120

Which indicates that critical point leads to an absolute maximum.

A current of 5 amperes will produce the maximum power.

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