The power generated by an electrical circuit (in watts) as a function of its current x xx (in amperes) is modeled by P ( x ) = − 15 x ( x − 8 ) P(x)=−15x(x−8)P, left parenthesis, x, right parenthesis, equals, minus, 15, x, left parenthesis, x, minus, 8, right parenthesis What current will produce the maximum power?

Given:

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

To find:

The current which will produce the maximum power.

Solution:

We have,

Differentiate with respect to x.

     ...(i)

To find the extreme point equate P'(x)=0.

Divide both sides by -30.

Differentiate (i) with respect to x.

(Maximum)

It means, the given function is maximum at x=4.

Therefore, the current of 4 amperes will produce the maximum power.

b.-4 units

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