document.write( "Question 1158623: Determine the location and value of the absolute extreme values of f on the given interval, if they exist.
\n" ); document.write( "f(x) =4sqrt(x) −8x^2/x
\n" ); document.write( "on [1,10] \n" ); document.write( "

Algebra.Com's Answer #854644 by KMST(5396) $\"\"$ $\"About$

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The function f(x)=4sqrt(x)−8x^2/x is not a very interesting one, and may not the the function intended.
\n" ); document.write( "I suspect the function intended could have been f(x)=(4sqrt(x)-8x^2)/x , which means $\"f%28x%29\"$ $\"%22=%22\"$ $\"%284sqrt%28x%29-8x%5E2%29%2Fx\"$ , also not an interesting function.\r
\n" ); document.write( "\n" ); document.write( "The domain of f(x)=(4sqrt(x)-8x^2)/x is $\"x%3E0\"$ , which can be expressed as $\"%22%280%2C%22\"$ $\"infinity\"$ $\"%22%29%22\"$ .
\n" ); document.write( "The graph of $\"f%28x%29\"$ $\"%22=%22%7D%7D%7B%7B%7B%284sqrt%28x%29-8x%5E2%29%2Fx\"$ $\"%22=%22\"$ $\"4%2Fsqrt%28x%29-8x\"$ is $\"graph%28300%2C200%2C-2%2C13%2C-90%2C10%2C%284sqrt%28x%29-8x%5E2%29%2Fx%29\"$
\n" ); document.write( "The derivative is negative throughout the domain of the function, meaning that the function decreases continuously.
\n" ); document.write( "Its absolute extremes in the interval [1, 10] are
\n" ); document.write( " $\"f%281%29\"$ $\"%22=%22\"$ $\"%284sqrt%281%29-8%2A1%5E2%29%2F1\"$ $\"%22=%22\"$ $\"%284%2A1-8%29%2F1\"$ $\"%22=%22\"$ $\"%284-8%29%2F1\"$ $\"%22=%22\"$ $\"%28-4%29%2F1=highlight%28-4%29\"$ , a maximum, and
\n" ); document.write( " $\"f%2810%29\"$ $\"%22=%22\"$ $\"%284sqrt%2810%29-8%2A10%5E2%29%2F10\"$ $\"%22=%22\"$ $\"%284sqrt%2810%29-8%2A100%29%2F10\"$ , a minimum, with a rounded value of $\"highlight%28-67.35%29\"$
\n" ); document.write( "
\n" ); document.write( "The domain of f(x)=4sqrt(x)−8x^2/x is $\"%22%280%2C%22\"$ $\"infinity\"$ $\"%22%29%22\"$ .
\n" ); document.write( "That function is $\"f%28x%29=4sqrt%28x%29\"$ $\"-8x%5E2%2Fx\"$ $\"%22=%22\"$ $\"system%284sqrt%28x%29-8x%2Cx%3E0%29\"$
\n" ); document.write( "Its graph is $\"graph%28300%2C200%2C-2%2C13%2C-90%2C10%2C4sqrt%28x%29-8x%29\"$
\n" ); document.write( "The derivative is negative throughout the domain of the function, meaning that the function decreases continuously.
\n" ); document.write( "Its absolute extremes in the interval [1, 10] are
\n" ); document.write( " $\"f%281%29=4sqrt%281%29-8%2A1=4%2A1-8=4-8=highlight%28-4%29\"$ , a maximum, and
\n" ); document.write( " $\"f%2810%29=4sqrt%2810%29-8%2A10=highlight%284sqrt%2810%29-8%29\"$ , a minimum, with a rounded value of $\"highlight%28-78.735%29\"$ \n" ); document.write( "

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