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Question

Find the minimum and maximum values of y in 4x2+12xy+10y44y+3=0

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Solution

4x2+12xy+10y44y+3=0
On differentiating, we get
8x+12xdydx+12y+40y3dydx4dydx=0
for max/min,dydx=0
so, 8x+12y=0
x=32y
Put in
f(x,y)=4x2+12xy+10y44y+3
max{f(x,y)}=9y218y2+10y44y+3
max{f(x,y)}=10y49y24y+3
which occurs at x=32y.
Hence, solved.


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