Find the linearization of the function at the given point.
-f(x, y) = -9x + 3y + 6 at (-2, 4)
A) L(x, y) = -2x + 4y + 6
B) L(x, y) = 18x + 12y + 36
C) L(x, y) = -9x + 3y + 6
D) L(x, y) = 18x + 12y + 6

Question

Quizplus · Accepted Answer

The linearization of a function at a given point is the equation of the tangent plane to the surface at that point. To find the linearization, we need to evaluate the function at the given point and its partial derivatives with respect to x and y at that point. 
f(-2, 4) = -9(-2) + 3(4) + 6 = 21
fx(-2, 4) = -9
fy(-2, 4) = 3
Using the formula for the equation of a plane, which is z - f(-2,4) = fx(-2,4)(x+2) + fy(-2,4)(y-4), we get
z - 21 = -9(x+2) + 3(y-4)
Simplifying this equation gives us:
z = -9x + 3y + 6, which is option C.

Find the Linearization of the Function at the Given Point