document.write( "Question 1089124: What is the interval where f(x)=lnx/x (x>0) decreases? \n" ); document.write( "

Algebra.Com's Answer #703456 by rothauserc(4718) $\"\"$ $\"About$

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f(x) = lnx/x
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\n" ); document.write( "f'(x) = (1 - ln(x)) / x^2
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\n" ); document.write( "set f'(x) = 0 and solve for x
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\n" ); document.write( "(1 - ln(x)) / x^2 = 0
\n" ); document.write( "ln(x) = 1
\n" ); document.write( "x = e
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\n" ); document.write( "at x = e, f(x) = 1/e, this is a global maximum
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\n" ); document.write( "f(x) decreases on (e, +infinity)
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\n" ); document.write( "Here is a graph of f(x)
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\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-6%2C+6%2C+-5%2C+5%2C+ln%28x%29%2Fx%29+\"$ \n" ); document.write( "

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