Consider the following function.
f(x, y, z) =
x2 + y2 + z2
Find
fx(x, y, z),
fy(x, y, z),
and
fz(x, y, z).
fx(x, y, z)
=
2x
fy(x, y, z)
=
2y
fz(x, y, z)
=
2z
Find the linear approximation of the function
f(x, y, z) =
x2 + y2 + z2
at
(4, 4, 7).
f(x, y, z) ≈
8x+8y+14z−81
Use the linear approximation to approximate the number
4.032 + 3.982 + 6.992
.
(Round your answer to four decimal places.)
f(4.03, 3.98, 6.99) ≈