You are told that the function f(x, y) = x6 + y - 6xy + 12 has fx(x, y) = 6x5 - 6y fy(x, y) = 6y' - 6x fxx (x, y) = 30x4 fxy (x, ) = -6 f vy = 30y4 Consider the point (1, 1). Which of the following statements is true? O A. f(x, y) has a saddle point at (1, 1). O B. (1, 1) is not a critical point of f(x, y). O c. f(x, y) has a relative maximum at (1, 1). O D. The second-derivative test yields no information. O E. f(x, y) has a relative minimum at (1, 1).x In(x) Consider the integral 1+ x2 dx. If we use integration by parts with u = In(x) then u = ... O ALL X O B. 2 In(1 + x2) O C. 2x In(1 + x2) O D. x In(x) - x O E. 1+ x2 OF. x+2x3 O G. ~ In(1 + x2)Waldo has built an empire of niche manufacturing, tourism, and agriculture businesses, andis building up capital for his next big venture: putting a goat on the moon. Every year, Waldo deposits $5000 into his Operation Goat Launchbank account. The account has an annual interest rate of 0.5% compounded continuously. There is currently $50000 in the account. Which of the following mathematical models best describes the amount of money in Waldo's account as a function of number of years t elapsed? O A. 21 = . dy = 0.5y + 5000t with y(1) = 50000 O B. at . dy = 0.005y + 50000 with y(1) = 5000 O C. ~ = 0.5y + 5000t with y(0) = 50000 OD. + dy = 0.005t + 5000 with y(0) = 50000 O E. ~ = 0.005y + 5000 with y(0) = 50000 OF. = = 0.005t + 5000y with y(1) = 50000