Find all the critical points and the absolute extrema(absolute maximum
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- Find the critical point of ƒ(x, y) = xy + 2x - ln x2y in the open first quadrant (x >0, y>0) and show that ƒ takes on a minimum there.Find the absolute maximum and absolute minimum values of the function f(x,y)=x2+y3 on the region bounded by x2+3y=4 and the x-axis.find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y R: The triangular region bounded below by the x-axis, above by the line y = x + 2, and on the right by the line x = 2.
- The critical point of f(x,y)=4x2+5xy+3y2 is the point (0,0). Classify this critical point: local maximum local minimum saddle point degenerate critical pointLet f(x, y) = cos(x)cos(y). Find all critical points of f which lie in the square {(x, y) ∈ R2 : −1 < x < 4 and − 1 < y < 4} and classify each as a local maximum, local minimum, or saddle point.Find the absolute maximum and minimum values of the function f(x, y) =2x2− 4x + 3y2 + 2 on the region R = {(x, y)|(x − 1)2 + y2 ≤ 1}. This uses Lagrange multipliers and the second derivative test to try and find the local extrema of these functions, but I don't know how to isolate one specific variable to solve this.
- find absolute maximum and minimum of f(x,y)=x^3+3xy-3y^2+2 in a region whose vertices at (-1,-1) (-1,1) (1,1) (1,-1)It posits only ∫ ∫ f(x,y)dA in the region bounded by; the x-axis, y - 2 = 0,y + x - 5 = 0 and x = y.Find the absolute minimum and absolute maximum of f(x,y)=19−9x+13y on the closed triangular region with vertices (0,0),(13,0) and (13,15). Minimum value: Occurs at: Maximum value: Occurs at:
- Find critical point (0,0) of f(x,y) =e^[(-2x^2)+(3y^2)] is a min, max, or saddle point using the second partials test.Find the absolute maximum and minimum values of f(x, y) = x^2 +xy + y^2 - 3x + 3y on the triangular region cut from the first quadrant by the linex + y = 4.Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).