document.write( "Question 1142067: Given that $\"y=8%2Fx%5E3\"$ , find the value of $\"dy%2Fdx\"$ when x = 2. Hence, without using a calculator, estimate the value of $\"8%2F2.001%5E3\"$ \n" ); document.write( "

Algebra.Com's Answer #762718 by Alan3354(69443) $\"\"$ $\"About$

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Given that $\"y=8%2Fx%5E3\"$ , find the value of $\"dy%2Fdx\"$ when x = 2.
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\n" ); document.write( " $\"f%28x%29=+8%2Fx%5E3\"$
\n" ); document.write( "f'(x) = $\"8%2A%28-3%29%2Ax%5E%28-4%29\"$
\n" ); document.write( "f'(2) = -24/16 = -3/2
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\n" ); document.write( "Hence, without using a calculator, estimate the value of $\"8%2F2.001%5E3\"$
\n" ); document.write( "= ~ 1
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\n" ); document.write( "Using linear \"interpolation\" --
\n" ); document.write( "Slope m = -3/2 = dy/dx
\n" ); document.write( "dx = 0.001
\n" ); document.write( "dy = -0.015
\n" ); document.write( "f(2.001) =~ 1 - 0.015 = 0.985\r
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