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Find the linear approximation of the function f(x, y, z) = x2 + y2 + z2 at (2, 9, 6) and use it to approximate the number 2.032 + 8.982 + 5.992 . (round your answer to five decimal places.)

Respuesta :

sqdancefan
At (x, y, z) = (2, 9, 6) the function is approximately
  f(x, y, z) = f(2, 9, 6) + 2·2·(x-2) + 2·9·(y-9) + 2·6·(z-6)
  f(x, y, z) = 121 + 4(x-2) +18(y-9) +12(z-6)

For your given numbers, the value of f(x, y, z) is approximately
  f(2.03, 8.98, 5.99) ≈ 121 + 4(.03) +18(-.02) +12(-.01)))
    = 121 +0.12 -0.36 -0.12 = 120.64

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