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

Question 233

Essay

A bug is crawling on the surface z=x2+xy+2y2z = x ^ { 2 } + x y + 2 y ^ { 2 } . When he reaches the point (2,1,8)( 2,1,8 ) he wants to avoid vertical change. In which direction should he head? (He wants the directional derivative in the ZZ -direction to be zero.)

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