find all critical points of the function f (x, y) = x³ + y³ – 3xy - and determine if they are local maxima or local minimal

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

A:

Q: If a and b are positive numbers, find the maximum value of f(x) = x(8 – x)º on the interval 0 < x <…

A: Given: f(x)=xa(8−x)b To find the maximum value find all the critical points. Critical points are…

Q: Find the absolute maxima and minima of f(x, y) = xy(18 – 2y - 9x) on the triangle bounded by the…

A: The function f(x,y)=xy(18-2y-9x)=18xy-2xy2-9x2y.  ∂f∂x=18y-2y2-18xy∂f∂y=18x-4xy-9x2 Find the points…

Q: Find the absolute maxima and minima for f(x) on the interval [a, b]. f(x) %3D 2x3 - 3х? - 36х — 3,…

A: We have to find the absolute maxima and minima for the function on the interval -10,10.…