Question

find the linearization L(x, y) of the function at that point
f (x, y )= tan^-1(x -2y) (1, 0)

Answer 1

Use implicit differentiation.

Find the zero's of f(x,y) = and f'(x,y) =
then, put it all into the linearization approximation, which is nothing more than the tangent line: \[L(x) = f(a) + f'(a)(x-a)\]