Let $h ( x , y , z ) = x ^ { 2 } - 2 x \sin y + z$ .Let $f ( x , y , z )$ satisfy $\nabla f ( 1,0,2 ) = \vec { i } - \vec { j } + 4 \vec { k }$ .Explain why the maximum of f subject to the constraint $h ( x , y , z ) = 3$ cannot occur at the point $( 1,0,2 )$ .

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The Answer of Let $h ( x , y , z ) = x ^ { 2 } - 2 x \sin y + z$ .Let $f ( x , y , z )$ satisfy $\nabla f ( 1,0,2 ) = \vec { i } - \vec { j } + 4 \vec { k }$ .Explain why the maximum of f subject to the constraint $h ( x , y , z ) = 3$ cannot occur at the point $( 1,0,2 )$ .

Let h(x,y,z)=x2−2xsin⁡y+zh ( x , y , z ) = x ^ { 2 } - 2 x \sin y + zh(x,y,z)=x2−2xsiny+z

Let $h ( x , y , z ) = x ^ { 2 } - 2 x \sin y + z$