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.)

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