Find the linear approximation of the function f(x, y) = ln(x - 3y) at point (7, 2)

Question

Find the linear approximation of the function f(x, y) = ln(x - 3y) at point (7, 2)

Answer 1

f(7,2 ) = ln(7 - 6) = 0

∂f/∂x = 1/(x - 3y); ∂f/dy = - 3/(x -3y). At (7, 2) ∂f/∂x = 1; ∂f/∂y = - 3

Linear approximation L(x,y) = 0 + 1(x - 0) - 3(y - 0) = x - 3y

L(x, y) = x - 3y