7:30 DAG . TO Ball 60% Conceptual Problems 6 1. True/False: Let f be differentiable at P. For any unit vector u, D_uf (P) = - Duf(P). 2. True/False: if f(x, y) = Iny, defined on those points (x, y) with y > 0, then Vf(x, y) = 1/y 3. True/ False: If Vf(x, y) = (0,0), then (x, y) is a local minimum or local maximum of f. 4. True/ False: if f is differentiable at (a, b) and Vf(a, b) = (0,0), then f has a local maximum or minimum at (a, b). 5. True/False: if f(x, y) has at least two local maxima then f must have a local minimum. (Hint: consider functions of the form f(x, y) = xmy".) 6. For f(x, y) = A - (x2 + Bx + y2 + Cy), what values of A, B, C give f a local maximum of 9 at the point (3, -1)? III O