Question

If f(x, y) =x^2-xy+y^2, determine ∇f(1,2) and use it to find the equation of the tangent line to the level curve f(x, y) = 7 at the point (1,2).

Answer 1

$\nabla f(x,y) = ((2x-y),(2y-x))$

$\nabla f(x,y)|_{(1,2)} = (0,3)$

Equation of tangent line will be

0(x-1) + 3(y-2) = 0,

y = 2 is the required equation.