Find the linearization of the function at the given point.
-$$f ( x , y , z ) = 7 x ^ { 2 } + 8 y ^ { 2 } + 7 z ^ { 2 } \text { at } ( 1 , - 2,3 )$$
A) L(x, y, z) = 14x - 32y + 42z - 102
B) L(x, y, z) = 14x + 32y + 42z - 102
C) L(x, y, z) = 14x + 32y + 42z + 102
D) L(x, y, z) = 14x - 32y + 42z + 102

Question

Quizplus · Accepted Answer

The linearization of a function at a point is given by the formula: L(x, y, z) = f(a, b, c) + fx(a, b, c)(x-a) + fy(a, b, c)(y-b) + fz(a, b, c)(z-c). Calculating the partial derivatives and evaluating at (1, -2, 3), we get L(x, y, z) = 14x - 32y + 42z - 102.

Find the Linearization of the Function at the Given Point f(x,y,z)=7x2+8y2+7z2 at (1,−2,3)f ( x , y , z ) = 7 x ^ { 2 } + 8 y ^ { 2 } + 7 z ^ { 2 } \text { at } ( 1 , - 2,3 )f(x,y,z)=7x2+8y2+7z2 at (1,−2,3)

Find the Linearization of the Function at the Given Point $f ( x , y , z ) = 7 x ^ { 2 } + 8 y ^ { 2 } + 7 z ^ { 2 } \text { at } ( 1 , - 2,3 )$