3. [-I3.12 Points] DETAILS SAPCALCBR1 7.1.010. Consider the function below. f(X, y) = |n(x + y 3) (a) Evaluate f(3, 1). E (b) Evaluate f(e, 3). :1 (c) Find the domain of f. O X > 3 Oy>3 Ox+y>3 OX+y3>1 OX>3,y>3 (d) Find the range of f. (Enter your answer using interval notation.) S ASK YOUR TEACHER MY NOTES SAPCALCBR1 7.1.019. DETAILS Plot the points (0, 0, 4), (1, 3, 0), (5, 1, -2), and (-1, 3, 4) on a single set of coordinate axes. 4. [-/3.12 Points] 12 0 0 2 - 2 N V N X A O A 2. O O 3.0 72.5 N 72.0 y O 12 2 1.5 A N y 1.0 O N 0 O N A O Submit Answer5. [-/3.12 Points] DETAILS SAPCALCBR1 7.2.014. Find the first partial derivatives of the function. f ( x, y ) = xy4 + 4x4y fx ( x, y) = fy ( x, y) = Submit Answer8. [-/3.12 Points] DETAILS SAPCALCBR1 7.2.028. Find the first partial derivatives of the function. f ( x, y, z) = x2yz3 + 5xy - 7z fx ( x, y, Z) = fy ( x, y, z) = fz ( x, y, Z) = Submit Answer9. [-/3.12 Points] DETAILS SAPCALCBR1 7.2.032. Find the first partial derivatives of the function. f( x, y, Z) = 3x v yz fx ( x, y, Z) = fy ( x, y, z) = fz ( x, y, Z) = Submit Answer Dines] DETAILS SAPCALCBR1 72.028. Find the first partial derivatives of the function.\f11. [-/3.12 Points] DETAILS SAPCALCBR1 7.2.044. MY NOTES ASK YOUR TEACHER Find all the second partial derivatives. u = x2y z4 Uxx ( X , y ) = Uxy ( X , y ) = Uyx ( x , y ) = Uyy ( x , y ) = Submit Answer 12. [-/3.12 Points] DETAILS SAPCALCBR1 7.3.006. MY NOTES ASK YOUR TEACHER Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f ( x, y) = x3y+ 36x2 - 8y local maximum value(s) local minimum value(s) saddle point(s) ( x, y, f ) = Submit Answer13. [-I3.12 Points] DETAILS SAPCALCBR1 7.3.008. Find the local maximum and minimum values and saddle point(s) of the function. If you have threedimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a commaseparated list. If an answer does not exist, enter DNE.) i'(x,y)=xy4x4yx2y2 local maximum value(s) local minimum value(s) saddle point(s) Submit Answer 14. [-/3.12 Points] DETAILS SAPCALCBR1 7.3.012. Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Mn0= f(x, y) = 4X3 + xy2 + 8x2 + y2 local maximum value(s) local minimum value(s) saddle point(s) Submit Answer Mn0= MYNOTES l ASKYOURTEACHEI MYNOTES l ASKYOURTEACHEI 15. [-/3.12 Points] DETAILS SAPCALCBR1 7.4.002. MY NOTES ASK YOUR TEACH Use Lagrange multipliers to find the maximum or minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f ( x, y) = 2xy; x2 + y2 = 4 maximum minimum Submit