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- A) Find the local maxinnun, local rninitnurn and saddle points of the function f(x,y)=8xy-y⁴-x⁴ B) Use Lagrange multipliers to find the local extreme values of f (x, y) = y²x on the line x+y=4The functionf(x, y, z) = x2+y+z an absolute maximum and absolute minimum subject to theconstraint 2x2+2y2+z2=2. Use Lagrange multipliers to find these values. I have tried a few ways to solve for the critical points, but they have all been incorrect.The finite region bounded by x=y^2 and x=6-2y^2 rotated around the line x=8. The region bounded by the x-axis, y=x^2 and y=2-x rotated around the x-axis. The region bounded by the x-axis, y=x^2 and y=2-x rotated around the y-axis.
- Considerthreemappingsα,β,γ:Z→Zdefined by α(n)=2n−1, β(n)=(n−1)^2, γ(n)=(n−1)^3Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the other two on the positive y-axis and the negative x-axis where the diagonal has length L = 3, occurs when the angles at both (other) vertices are π/4. Include a sketch.Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y) = xy subject to 3x + y = 42. fmax = Also find the corresponding point (x, y). (x, y) =
- Determine the value of x within the interval (0, 1) that minimizes the function f = (x –1)(x –2.5) to within ± 0.025 by .(a) the Fibonacci method and (b) the golden section method.find the orthogonal trajectories of the family ofcurves. Sketch several members of each family. 2x2 + y2 = c2Find the optimum of f(x) = 2.2x – 1.7x2 + x3 – 0.25x4 Perform: (Round-off all computed values to 4 decimal places.)a) (2 iterations) Golden-Section Search using XL = –2.4 and XU = 4.5 For each iteration, show the following: d, X1, X2, decision rule, ea, and the next XL andXU Are you approaching a local or global optimum? ____________ Are you approaching a minimum or maximum optimum? __________
- Use Lagrange multipliers to find the global minimum and maximum of the provided function f(x,y) on the provided region R: f(x,y) = x3-3x-y3+12y on the quadrilateral R with vertices (-2,3), (2,3), (2,2), and (-2,-2) (See attatched image for hint)Fast pls solve this question correctly in 5 min pls I will give u like for sure Mnty Use Lagrange multipliers to maximize f (x, y) = 3x + 5xy + 6y subject to the constraint x + 2y = 4.a)The formula of calculating an upper bound of theabsolute error in bisection method is stronger thanthose of the fixed point iteration.Select one:TrueFalse b)Let g(x) = x2 – 2x – 4 on [-2, 4] , then the fixedpoints for g(x) are:Select one:a. -1 and 4b.-1C. 4d. -1 and -4 c) The number of iterations necessary to achieve an accuracy 10-2using bisection method on theinterval [0,2] is:Select one:a. 6b. 8c. 7d. 5 d)Secant Method is faster than Newton RaphsonMethod.Select one:a. Yesb. No e) The fractional part (mantissa) of the machinenumber0 01100000111 01010011000 isSelect one:a. 0.32980b. 0.72421875c. 0.32421875d. 0.421875