A bug is crawling on the surface $z = x ^ { 2 } + x y + 2 y ^ { 2 }$ . When he reaches the point $( 2,1,8 )$ he wants to avoid vertical change. In which direction should he head? (He wants the directional derivative in the $Z$ -direction to be zero.)

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The Answer of A bug is crawling on the surface $z = x ^ { 2 } + x y + 2 y ^ { 2 }$ . When he reaches the point $( 2,1,8 )$ he wants to avoid vertical change. In which direction should he head? (He wants the directional derivative in the $Z$ -direction to be zero.)

A Bug Is Crawling on the Surface z=x2+xy+2y2z = x ^ { 2 } + x y + 2 y ^ { 2 }z=x2+xy+2y2

A Bug Is Crawling on the Surface $z = x ^ { 2 } + x y + 2 y ^ { 2 }$