document.write( "Question 1030357: Optimization\r
\n" ); document.write( "\n" ); document.write( "The power absorbed by a circuit is p(x) = ((V^2)x)/(R+x)^2 where R is the resistance in ohms and V is the voltage in volts. Find the value of x that maximizes the power absorbed. \n" ); document.write( "

Algebra.Com's Answer #645322 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the derivative, I'm substituting a and b for the constants for better readability,
\n" ); document.write( " $\"p=%28ax%29%2F%28b%2Bx%29%5E2\"$
\n" ); document.write( " $\"dp%2Fdx=%28%28b%2Bx%29%5E2%2Aa-2ax%28b%2Bx%29%29%2F%28b%2Bx%29%5E4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"dp%2Fdx=%28a%2F%28b%2Bx%29%5E4%29%28b%5E2%2B2bx%2Bx%5E2-2bx-2x%5E2%29\"$
\n" ); document.write( " $\"dp%2Fdx=%28a%2F%28b%2Bx%29%5E4%29%28b%5E2-x%5E2%29\"$
\n" ); document.write( " $\"dp%2Fdx=%28a%2F%28b%2Bx%29%5E4%29%28b-x%29%28b%2Bx%29\"$
\n" ); document.write( " $\"dp%2Fdx=%28a%28b-x%29%29%2F%28b%2Bx%29%5E3\"$
\n" ); document.write( " $\"dp%2Fdx=%28V%5E2%28R-x%29%29%2F%28R%2Bx%29%5E3\"$
\n" ); document.write( "So then when the derivative equals zero,
\n" ); document.write( " $\"x=R\"$
\n" ); document.write( "and
\n" ); document.write( " $\"p=%28V%5E2%2AR%29%2F%28R%2BR%29%5E2\"$
\n" ); document.write( " $\"p=%28V%5E2%2AR%29%2F%284R%5E2%29\"$
\n" ); document.write( " $\"p=V%5E2%2F%284R%29\"$
\n" ); document.write( " \n" ); document.write( "

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