What is the minimum value of the function f(x,y)= x^2+y^2 -y on the region where y greater or equal x^2 and y smaller or equal 1

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math calculus

Answer 1

Answer #1

f(x,y)= x^2+y^2 -y

Find partial derivative as

fx= 2x

fy=2y -1

To find critical point, set fx =0 and fy=0

2x =0, so x =0

2y-1=0, so y=1/2

Hence, critical point is (0, 1/2)

f(0, 1/2)= 0^2+(1/2)^2 -(1/2)= -1/4

minimum value of the function is -1/4

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Answer 2

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