document.write( "Question 977588: The concentration of a drug in a bloodstream, measured in milligrams per liter, can be modeled by the function, C(t)=(12t+4)/(3t²+2), where t is the number of minutes after injection of the drug. When will the drug be at its highest concentration? Approximate your answer rounded to two decimal places. \n" ); document.write( "

Algebra.Com's Answer #599127 by Fombitz(32388) $\"\"$ $\"About$

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Find the derivative,
\n" ); document.write( " $\"dC%2Fdt=%28%283t%5E2%2B2%2912-%2812t%2B4%29%286t%29%29%2F%283t%5E2%2B2%29%5E2\"$
\n" ); document.write( " $\"dC%2Fdt=%2836t%5E2%2B24-72t%5E2-24t%29%2F%283t%5E2%2B2%29%5E2\"$
\n" ); document.write( " $\"dC%2Fdt=%28-36t%5E2-24t%2B24%29%2F%283t%5E2%2B2%29%5E2\"$
\n" ); document.write( " $\"dC%2Fdt=%28-12%283t%5E2%2B2t-2%29%29%2F%283t%5E2%2B2%29%5E2\"$
\n" ); document.write( "Set the derivative equal to zero.
\n" ); document.write( " $\"3t%5E2%2B2t-2=0\"$
\n" ); document.write( " $\"t%5E2%2B%282%2F3%29t-2%2F3=0\"$
\n" ); document.write( " $\"t%5E2%2B%282%2F3%29t%2B1%2F9=2%2F3%2B1%2F9\"$
\n" ); document.write( " $\"%28t%2B1%2F3%29%5E2=7%2F9\"$
\n" ); document.write( " $\"t%2B1%2F3=0+%2B-+sqrt%287%29%2F3\"$
\n" ); document.write( " $\"t=-1%2F3+%2B-+sqrt%287%29%2F3\"$
\n" ); document.write( "Only use the positive time value.
\n" ); document.write( " $\"t=-1%2F3+%2B+sqrt%287%29%2F3\"$
\n" ); document.write( " \n" ); document.write( "

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