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- Test the functions in Exercises 65–68 for local maxima and minima and saddle points. Find each function’s value at these points. 65. . ƒ(x, y) = 2x3 + 3xy + 2y3 66. ƒ(x, y) = x3 + y3 - 3xy + 15 67. ƒ(x, y) = x3 + y3 + 3x2 - 3y2 68. ƒ(x, y) = x4 - 8x2 + 3y2 - 6yTest the functions in Exercises 65–66 for local maxima and minima and saddle points. Find each function’s value at these points. 65. ƒ(x, y) = x2 - xy + y2 + 2x + 2y - 4 66. ƒ(x, y) = 5x2 + 4xy - 2y2 + 4x - 4yMaximizing Production Suppose that the output of the finished product (x, y) of a company is described by the Cobb-Douglas production function (x, y) - axy! - b where x is the amount of money expended on labor, y is the amount expended on capital, and a and b are positive constants with 0A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by the parabolas x = y²and y = x². Region C is bounded by the parabola y = x², the line x = 1, and the x-axis.Find the maximum and minimum outputs for f(x,y) = x^2y-x+y^2 on the set D= (x,y){ -2(less than or equal to)x(greater or equal to)2}, {-1(less than or equal to)y(greater than or equal to)2 } Solving using langrange multipliers, (y=x^2 is the graph ) Was wondering how to solve it completely & what langrage multipliers help us achieve, (my thinking is the max & min) of the function f without having to do it the other way where you find corner points, boundary points & critical points, thank you :)Consider the following. - 2x2 + 3x + 2 y Find the relative maxima, relative minima, and points of inflection. (If an answer does not exist, enter DNE.) relative maxima (x, y) = (| relative minima (х, у) 3D points of inflection (x, y) =True or false and why? Explain. The linearization of f(x,y) = 5 + 7x + 3y at any point (a,b) is the function L(x,y) = 5 + 7x + 3y.The domain of the function f(x,y) =, ху is V x² + y? The upper half plane without the origin The second and the fourth quadrant without the origin The first and the third quadrant without the origin The left right plane without the originAdditional Activities (-2, 39) (14) 43 -2 -1 (-5, -42) 5 8 8 8 8 20 10 10 -20 -30 40 (2.7) 3 B. Locate and classify the critical point of y = x³ - 2x² - 6x + 2.Differentiability of f(x,y). [Part 2]Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) x² y = X² + 3 intercept (х, у) 3D relative minimum (x, y) = relative maximum (x, y) = points of inflection (x, y) = (smaller x-value) (x, y) = (larger x-value) Find the equation of the asymptote. Use a graphing utility to verify your results.Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) x2 y = x2 + 243 intercept (x, y) = relative minimum (x, y) | relative maximum (x, y) = points of inflection (x, y) = (smaller x-value) (x, y) = (larger x-value) Find the equation of the asymptote. Use a graphing utility to verify your results. y y X - 30 -20 to 10 20 30 - 30 - 20 -10 20 30 -2t -2t y y 2.0 -30 - 20 -10 10 20 30 1.5 -0.5 1.0 0.5 -1.5 -2.0 - 30 -20 -10 10 20 30SEE MORE QUESTIONS