, Let f(x, y) = x + y. (1) Find fx (x, y) and fx (x, y): Denote fx (x, y) = x2 x + y and fy(x, y) = x2 x + y then p = y 9 = (2) Evaluate the partial derivatives: fx (3, 4) 3/5 fy (3, 4) = 4/5 fx (4,3) = = 4/5 = 3/5 fy(4, 3) = (input most simplified fractions) (3) The linear approximation of f(x, y) at (xo, yo) is a function linear on both x and y, - L(x, y) = f(xo, Yo) + fx (xo, Yo)(x x0) + fy(x In order to use the linear approximation to estimate f(3.04, 3.98), using the partial derivative values computed above, you would choose x0 = 4 3 , Yo = Then you get L(3.04, 3.98) 4.642 =