Suppose that a function f x , y , z is differentiable at the point 3 , 2 , 1 and L x , y , z = x − y + 2 z − 2 is the local linear approximation to f at 3 , 2 , 1 . Find f 3 , 2 , 1 , f x 3 , 2 , 1 , f y 3 , 2 , 1 , and f z 3 , 2 , 1 .
Suppose that a function f x , y , z is differentiable at the point 3 , 2 , 1 and L x , y , z = x − y + 2 z − 2 is the local linear approximation to f at 3 , 2 , 1 . Find f 3 , 2 , 1 , f x 3 , 2 , 1 , f y 3 , 2 , 1 , and f z 3 , 2 , 1 .
Suppose that a function
f
x
,
y
,
z
is differentiable at the point
3
,
2
,
1
and
L
x
,
y
,
z
=
x
−
y
+
2
z
−
2
is the local linear approximation to f at
3
,
2
,
1
.
Find
f
3
,
2
,
1
,
f
x
3
,
2
,
1
,
f
y
3
,
2
,
1
,
and
f
z
3
,
2
,
1
.
Calculate fz(3, 6, 9), where f(x, y, z) = xyz.
fz(3, 6, 9) =
Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable function z = z (x, y). Express az/ ax and az/ay in terms of x, y, z
Precalculus Enhanced with Graphing Utilities (7th Edition)
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