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f(x,y,z)=4x^2+4y^2+z^2 subject to x^2+y^2+z^z=1

So I have:

F(x,y,z,c) = 4x^2+4y^2+z^2+L(x^2+y^2+z^2-1)

dF/dx = 8x+2xL

dF/dy = 8y+2yL

dF/dz=2z+2zL

Either x=y=0 and L=-1 OR z=0 and L=-4

For first case, z^2=1 therefore z=+/- 1 giving f(0,0,1)=1

For second case, x^2+y^2=1 2x^2=1 x=y=+/-sqrt(1/2) giving f(sqrt(1/2),sqrt(1/2),0)=4

Is this correct?

The minimum is therefore the first case giving f(0,0,1)=1?

So I have:

F(x,y,z,c) = 4x^2+4y^2+z^2+L(x^2+y^2+z^2-1)

dF/dx = 8x+2xL

dF/dy = 8y+2yL

dF/dz=2z+2zL

Either x=y=0 and L=-1 OR z=0 and L=-4

For first case, z^2=1 therefore z=+/- 1 giving f(0,0,1)=1

For second case, x^2+y^2=1 2x^2=1 x=y=+/-sqrt(1/2) giving f(sqrt(1/2),sqrt(1/2),0)=4

Is this correct?

The minimum is therefore the first case giving f(0,0,1)=1?

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