anonymous
  • anonymous
Partial differentials/Linear approx. Given that f is a differentiable function with f(2,5)=6, fx(2,5)=1 and fy(2,5)=-1, use a linear approx. to estimate f(2.2, 4.9)
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
According to the solution manual, the answer is 6.3. I can't seem to get that answer...
amistre64
  • amistre64
i know it follows a taylor feel \[f(x,y)\approx f+fx~x+fy~y\] but im missing something
anonymous
  • anonymous
You do this:\[L(x^*,y^*)=[f_x(x_0,y_0)](x^*-x_0)+[f_y(x_0,y_0)](y^*-y_0)+z_0\] where L is the approximation function, with value at the *'s and the 0's is the original point

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amistre64
  • amistre64
fx(x-xo) +fy(y-yo) = 0 fx(x-2) +fy(y-5) = 0 (x-2) - (y-5) = 0
amistre64
  • amistre64
gives me .3, so the 6 needs to be applied
amistre64
  • amistre64
f + fx(x-2) +fy(y-5) gives us 6.3

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