The question I'm stuck on is this: Let [tex]f(x,y) = (x+1)^2 + y^2[/tex] I'm asked to find the partial derivatives and then evaluate them at (1,2). From there, find L(x,y), the linear approximation to f(x,y) at (1,2). That part I'm ok with. I got the following: [tex]f_x(x,y) = 2(x+1)[/tex] [tex]f_y(x,y) = 2y[/tex] [tex]f_x(1,2) = 4[/tex] [tex]f_y(1,2) = 4[/tex] [tex]f(1,2) = 8[/tex] [tex]L(x,y) = 8 + 4(x-1) + 4(y-2)[/tex] Next part of the quesion was just filling in a table that shows that as f(x,y) moves away from (1,2), L(x,y) becomes less accurate approximation of f(x,y). So where am I stuck? On the last question, which is: "On a set of xy-axes, mark the point (1,2) and draw the level curves f(x,y) = k and L(x,y) = k for k = 5, 6, 7, 8, 9, 10. Draw the curves into the square [0,3]x[0,3] and label each curve with the value of k. How do the level curves reflect L' approximation of f near (1,2)?" This is likely a very easy question to do, but for the life of me I can't see how! Any (and all) help much appreciated.