MATH 2433 Online - Fall 2015 Homework Week 7 Instructions Homework will NOT be accepted through email or in person. Homework must be submitted through CourseWare BEFORE the deadline. Submit the multiple choice section of the assignment at http://www.casa.uh.edu under "EMCF" and choose ehw 7. y) 1. What is the maximum value of f ( x,= 4 x 2 y 2 on the region where x 2 + y 2 1 ? a. 4 b. 2 c. -1 d. -2 e. 0 f. None of these 2. What is the maximum value of f ( x, y ) = x 2 x y on the region where {( x, y ) : 0 x 1, 0 y 1} ? a. b. c. d. e. f. -2 -3/2 -5/4 -1 -3/4 None of these { } 3. What is the maximum value of f ( x,= y ( x 3) on the region where ( x, y ) : x 2 + y 2 9 ? y) a. b. c. d. e. 27 4 27 4 27 3 4 27 3 4 None of these { } 4. What is the minimum value of f ( x,= y ( x 3) on the region where ( x, y ) : x 2 + y 2 9 ? y) 27 4 27 b. 4 27 3 c. 4 27 3 d. 4 e. None of these 5. Find the minimum value of f ( x, y ) = ( x 1) 2 + ( y 4) 2 + (3 x 2 y ) 2 a. 0 b. 1 c. 3 d. 6 e. -1 f. None of these 12 6. Find the maximum value of the function f ( x, y, z ) = xyz on the sphere x 2 + y 2 + z 2 =. a. -8 b. -4 c. 0 d. 4 e. 8 f. None of these a. 1. 7. Maximize x 2 + y 2 on the curve x 4 + 7 x 2 y 2 + y 4 = The maximum is: a. 1 2 b. 3 3 c. 3 d. -1 e. None of these 8. Find the distance from the point (0, 1) to the parabola x 2 = 4 y . a. 0 b. 1 c. 2 3 d. 4 e. None of these 9. Give the equation of the normal line to ( y x) 2 x = at the point P(1, 2) . 8 a. 5 x 6 y = 17 b. 5 x + 6 y = 7 c. 6 x + 5 y = 4 d. 5 x 6 y = 17 e. 10. An equation for the tangent plane to the surface the surface is: a. b. c. d. e. none of these at the point P(2, -1,1) on 11. The stationary point(s) of the function = 2 + 3 2 2 8 + 5 are: 3 a. (4, 1) and (-1, 2) b. (1, 0) and (3, 2) c. (1, 2) and (-1, 4) d. (1, 4) and (1, -2) e. None of the above 12. The stationary point (1, 4) of the function a. Local maximum b. Local minimum c. Saddle point 13. The boundary of the disc a. b. c. d. x(t ) = 4 cos t , y (t ) = 4sin t , 0 t 2 e. none of these 1 is a can be parameterized as: 14. An equation for the tangent plane to the surface z 2 xy 2 = surface is: a. b. c. 12 x + 6 y z = 20 d. e. none of these 2y at the point P(1, 2, 4) on the x 15. Scalar parametric equations for the normal line to the surface z 2 xy 2 = P(1, 2, 4) on the surface is: a. b. c. d. x = 12t , y = 6t , z = t 1+ 2+ 4 e. none of these 2y at the point x