MATH 3C - SECTION 3.8 HOMEWORK Laney College, Spring 2023 Fred Bourgoin Problems #1-2 refer to the figure below. 1. Which of points A, B, and C appear to be critical points? Classify those that are critical points. 2. Which of points D G appear to be local maxima? Local minima? Saddle points? In #3 6, the function has a critical point at (0, 0). What kind of critical point is it? 3. f(x,y) = 12 - cosy 5. f(x,y) = 24 +3 4. f(x, y) = xsiny 6. f(x,y) = 2 + y In #7-12, Find the critical points of the given function and classify them as local max- ima, local minima, saddle points, or none of these. 7. f(x,y) = x2 - 2xy + 3y2 - 8y 8. f(x,y) =5+6x - x2 + xy - y2 9. f(x, y) = x2 - y? + 4x + 2y 10. f(x, y) = 400 - 3x2 - 4x + 2xy - 5y? + 48y 11. f(x,y) = 13 - 3x + y3 - 3y 12. f(x,y) = (x + y)(ry+ 1) 13. Let f(x,y) = 3x2 + ky2 + 9ry. Determine the values of k (if any) for which the critical point (0, 0) is : (a) A saddle point (b) A local maximum (c) A local minimum 14. Find A and B so that f(x, y) = x2 + Ar + y? + B has a local minimum value of 20 at (1, 0)