SOLUTION: Given that {{{y=8/x^3}}}, find the value of {{{dy/dx}}} when x = 2. Hence, without using a calculator, estimate the value of {{{8/2.001^3}}}

Algebra ->  Expressions-with-variables -> SOLUTION: Given that {{{y=8/x^3}}}, find the value of {{{dy/dx}}} when x = 2. Hence, without using a calculator, estimate the value of {{{8/2.001^3}}}      Log On


   

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
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given that y=8%2Fx%5E3, find the value of dy%2Fdx when x = 2.
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f%28x%29=+8%2Fx%5E3
f'(x) = 8%2A%28-3%29%2Ax%5E%28-4%29
f'(2) = -24/16 = -3/2
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Hence, without using a calculator, estimate the value of 8%2F2.001%5E3
= ~ 1
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Using linear "interpolation" --
Slope m = -3/2 = dy/dx
dx = 0.001
dy = -0.015
f(2.001) =~ 1 - 0.015 = 0.985