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November 1st, 2011, 03:42 PM   #1
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need help with linear approximation problem

Use linear approximation to estimate the value of f(3.1), given that f(3)=9 and f '(x) = (5x^2) / (sqrt(x^3-2))

Please help !
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November 2nd, 2011, 12:32 AM   #2
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Re: need help with linear approximation problem

f(x+dx) = f(x) + ( f ' (x) )*dx approximately
x+dx = 3.1
x =3
dx =0.1
f(x) = f(3) = 9
compute f ' (x) = f ' (3) thanks to the given formula
then compute f(x) + ( f ' (x) )*dx
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November 2nd, 2011, 01:33 AM   #3
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Re: need help with linear approximation problem



Let . Then:

Integral becomes

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November 2nd, 2011, 01:35 AM   #4
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Re: need help with linear approximation problem

Sorry I went wrong with the last step.
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November 2nd, 2011, 03:11 AM   #5
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Re: need help with linear approximation problem

Hello Etyucan,
you forgot the integration constant.
The correct analytical result is : 9+(10/3)sqrt[(x^3)-2] - (10/3)sqrt[(3^3)-2]
= (10/3)sqrt[(x^3)-2] -(23/3)
= 9.90572329283767 for x=3.1
But isn't what pdeep needs to answer to his problem. Linear approximation is much simpler and suffisant : the resul is close to the exact value.
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