Let fx y 3xx32y2y4 on the domain D x y 5

Let f(x, y) = 3x-x^3-2y^2+y^4 on the domain D = {(x, y)| -5<=x<= 5, -2<=y <=2}. Find all critical points and use the second derivative test to determine whether they are absolute, local maxima, minima or neither. Please show step by step.

f(x,y) = 3 - 3x² = 0

x = ±1

x = 1 maxima

x = -1 minima

partial diff wrt y : 4y³ - -4y = 0

y = 0 , ±1

y = 0 maxima

y = 1 minima

y = -1 minima

(1,0) = 2 local maxima

(-1,1) = -1 local minima

(-1,-1) = -1 local minima

(1, 1) , (1 , -1) , (-1 , 0) neither !!!

global maxima (-5 , 2)

global minima (5 , -2)

end points ~~~

$Let f(x, y) = 3x-x^3-2y^2+y^4 on the domain D = {(x, y)| -5<=x<= 5, -2<=y <=2}. Find all critical points and use the second derivative test to deter$

Let fx y 3xx32y2y4 on the domain D x y 5

Solution

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