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Find the gradient of the function g(x,y) = xy at the point (1, - 2). Then sketch the gradient together with the level curve that passes through the point. First find the gradient vector at (1, - 2). Vg(1, - 2) = 4 i+ ( -4 )j (Simplify your answers.) Choose the graph that shows the level curve and the gradient vector at (1, - 2). O A. O B. O C. OD. HHHHHH THFind the gradient of the function f(x,y) = 2x + 4y at the point ( - 2,2). Then sketch the gradient together with the level curve that passes through the point. Vil(-2,2) = 5 1+ 1j (Type integers or simplified fractions.) Choose the correct graph below. O A. O B. O C. OD. A A _AY 5 5 5Solve the initial value problem for r as a vector function oft. d Differential equation: F: = 3"t i j 3t k Initial condition: rm}: 5i +j + 9k riti=iii+i+iik Find the derivative of the function at Po in the direction of A. f(x,y) = - 3xy - 5y , Po(1, -1), A=i+ 5j (DAn) (1 - 1) = (Type an exact answer, using radicals as needed.)Find the derivative of the function at P in the direction of A. f(x, y,z) = xy + yz + zx, Po(2, - 2, - 3), A = 2i + 3j -6k (DAf) (2. -2, -3) = (Simplify your answer.)In which direction does the function increase most rapidly? 1= ) k (Type exact answers, using radicals as needed.) In which direction does the function decrease most rapidly? -1= (Type exact answers, using radicals as needed.) What is the value of the derivative in the direction of u? (Duf)Po (Type an exact answer, using radicals as needed.) What is the value of the derivative in the direction of - u? (D -uf)p.Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions. f(x,y,z) = (x/y) - yz, Po(-3,1, - 1)