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Use technology to answer parts (a) through (d) about the function f(x,y) =x-+y -5xy for - 300 sxs 300 and - 60 sy = 60. a. Plot some level curves in the given rectangle. b. Calculate the function's first partial derivatives and find the critical points. How do the critical points relate to the level curves plotted in part (a)? Which critical points, if any, appear to give a saddle point? Give reasons for your answer. c. Calculate the function's second partial derivatives and find the discriminant fxxfyy - fxy d. Using the max-min tests, classify the critical points found in part (b). Are your findings consistent with your reasons in part (b)?Find the absolute maximum and minimum of the function f(x.y) = (40x - 10x ) cosy on the rectangular plate 1 s x= 3, - - Sys -Solve by the substitution method. 9x + 4y = - 15 x = 15 - 6y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set of the system is (Simplify your answer. Type an ordered pair.) O B. There are infinitely many solutions. O C. The solution set is the empty set.Find all the local maxima, local minima, and saddle points of the function. f(x,y) = By sin (x) Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. A local maximum occurs at , where n is any integer. (Type an ordered pair. Type an expression using n as the variable. Use a comma to separate answers as needed.) The local maximum value(s) is/are (Type an exact answer. Use a comma to separate answers as needed.) B. There are no local maxima. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. A local minimum occurs at , where n is any integer. (Type an ordered pair. Type an expression using n as the variable. Use a comma to separate answers as needed.) The local minimum value(s) is/are (Type an exact answer. Use a comma to separate answers as needed.) B. There are no local minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. A saddle point occurs at , where n is any integer. (Type an ordered pair. Type an expression using n as the variable. Use a comma to separate answers as needed.) O B. There are no saddle points