QUESTION 1

Find f (x,y) and f(x,y). Then find fx (2, - 1) and fy (1, 1). f(x,y) = - ge 2x - 5y fx (x, y) = fv (x,y) = fx (2, - 1) = (Type an exact answer.) fy (1, 1) = (Type an exact answer.)8 Use the properties of definite integrals to find f(x) dx for the following function. 6 4x + 7 if x$7 f(x) = -0.2x +7 ifx> 7 8 f ( x ) dx = 6 (Simplify your answer.)For the function defined as follows, find all values of x and y such that both f (x,y) = 0 and fy (x, y) = 0. f (x, y) =2x + 6y +5xy+ 35x - 9 . . . Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There are two solutions where f (x,y) = 0 and fv(x,y) = 0, in order from increasing x values, when x = and y = and X = and y = (Type integers or simplified fractions.) O B. There is only one solution where fx(x,y) = 0 and f(x,y) = 0, when x = and y = (Type integers or simplified fractions.) O C. There are three solutions where f (x,y) = 0 and fv(x,y) = 0, in order from increasing x values, when x = and y = and x = and y = and x = and y = (Type integers or simplified fractions.) O D. There are no solutions where f (x,y) = 0 and fy (x,y) = 0.For the function f(x,y) = 4.} y2 + 5x2 , nd f(2, - 4), f( - 3,5), f( - 2, - 1), and f(0,?). f(2, -4) = E (Type an exact answer, using radicals as needed.) f(- 3,5) = D (Type an exact answer, using radicals as needed.) f(- 2, - 1): (Type an exact answer, using radicals as needed.) f(0,7}= (Type an exact answer, using radicals as needed.) Find the area between the curves. x = -3, x=3, y=2e", y=e2* + 1 The area between the curves is approximately (Do not round until the final answer. Then round to the nearest hundredth as needed.)