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x^2+(y-1)^2=1 (1)
2x + 2(y-1).dy/dx = 0
dy/dx = -x/(y-1)
S=2x+y
dS/dx
=2 + dy/dx
=2 -x/(y-1)
dS/dx =0
2 -x/(y-1) =0
2(y-1) -x =0
y= (x+2)/2 (2)
sub (2) into (1)
x^2+(y-1)^2=1
x^2+((x+2)/2-1)^2=1
4x^2=4
x= 1 or -1
x=1, y=3/2 (max)
x=-1, y = 1/2 (min)
S=2x+y
max S = 2(1) + 3/2 = 7/2
min S = 2(-1) + 1/2 = - 3/2
2x + 2(y-1).dy/dx = 0
dy/dx = -x/(y-1)
S=2x+y
dS/dx
=2 + dy/dx
=2 -x/(y-1)
dS/dx =0
2 -x/(y-1) =0
2(y-1) -x =0
y= (x+2)/2 (2)
sub (2) into (1)
x^2+(y-1)^2=1
x^2+((x+2)/2-1)^2=1
4x^2=4
x= 1 or -1
x=1, y=3/2 (max)
x=-1, y = 1/2 (min)
S=2x+y
max S = 2(1) + 3/2 = 7/2
min S = 2(-1) + 1/2 = - 3/2
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