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Firdavs [7]
3 years ago
11

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?
Mathematics
1 answer:
marysya [2.9K]3 years ago
7 0

Given:

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

P(x)=-15x(x-8)

To find:

The current which will produce the maximum power.

Solution:

We have,

P(x)=-15x(x-8)

P(x)=-15x^2+120x

Differentiate with respect to x.

P'(x)=-15(2x)+120(1)

P'(x)=-30x+120      ...(i)

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

-30x+120=0

-30x=-120

Divide both sides by -30.

x=4

Differentiate (i) with respect to x.

P'(x)=-30(1)+(0)

P'(x)=-30 (Maximum)

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

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

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