As discussed in the text, a function f (x, y) may have partial derivatives fx (a...

As discussed in the text, a function f (x, y) may have partial derivatives fx (a, b) and fy (a, b) yet fail to be differentiable at (a, b). Geometrically, if a function f (x, y) is differentiable at (a, b), then, aswe zoom in on the point (a, b, f (a, b)), the graph of z = f (x, y) will “flatten out” and look like the plane given by equation (4) in this section. For the functions f (x, y) given in Exercises 53–57, (a) calculate fx (a, b) and fy (a, b) at the indicated point (a, b) and write the equation for the plane given by formula (4) of this section, (b) use a computer to graph the equation z = f (x, y) together with the plane calculated in part (a). Zoom in near the point (a, b, f (a, b)) and discuss whether or not f (x, y) is differentiable at (a, b). (c) Give an analytic (i.e., nongraphical) argument for your answer in part (b).