document.write( "Question 1200978: This is from my derivatives of exponents lesson.\r
\n" ); document.write( "\n" ); document.write( "If f(x)=10^(3x-5) times e^[(2x)^2], determine the values of x so that f'(x)=0.\r
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Algebra.Com's Answer #835202 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        This my post is a correction to the solution by @psbhowmick.\r
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\n" ); document.write( "\n" ); document.write( "f(x) = \"10%5E%283x-5%29e%5E%28%282x%29%5E2%29\" = \"10%5E%283x-5%29e%5E%284x%5E2%29\".\r
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\n" ); document.write( "\n" ); document.write( "\"d%28f%28x%29%29%2Fdx\" = \"10%5E%283x-5%29e%5E%284x%5E2%29%2A8x\" + \"10%5E%283x-5%293ln%2810%29%2Ae%5E%284x%5E2%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"d%28f%28x%29%29%2Fdx\" = \"10%5E%283x-5%29e%5E%28%282x%29%5E2%29%2A%288x%2B3ln%2810%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"d%28f%28x%29%29%2Fdx\" = \"10%5E%283x-5%29%2Ae%5E%28%282x%29%5E2%29%2A%288x%2Bln%281000%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "        Clearly,   \"d%28f%28x%29%29%2Fdx\"   will be zero only if   \"8x%2Bln%281000%29\"   is zero.\r
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\n" ); document.write( "\n" ); document.write( "8x + ln(1000) = 0\r
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\n" ); document.write( "\n" ); document.write( "x = \"%28-1%2F8%29ln%281000%29\" = -0.86346941.             ANSWER\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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