3. (a) Find an example of a function f of two variables for which Vf = (3, 2). That is, we want the gradient to be equal to this vector at every point. (b) Consider the graph = = f(x, y) for your function, which we can think of as a two-dimensional surface in three dimensional space. The graph is a familiar geometric object - but what kind? (c) Is there any point (a, b) at which some directional derivative Duf (a, b) is equal to 4? 4. (a) Consider the equation e' = r + y' try'. Use implicit differentiation to find What is equal Or to at the point (0, 1, 0)? (b) Now, let z = In(x + y* + ry?). Find Oz What is equal to if r = 0 and y = 1? (c) Explain why the two values you computed in the previous parts should be the same. (d) Plugging (x, y, =) = (1, 1,3) into the two formulas you found for az Or in the first two parts will not give the same answer. What makes this situation different from what happened in the previous part