SolutionExam2_5C - Math 5C Midterm Exam#2 Summer 2014 Name...

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Math 5C Midterm Exam #2Summer 2014Name:Date:Signature:Instructions:1. Please show all work. No work or little work may lead to no credit or little credit.2. No calculator, book or notes allowed.1
1:(20 Points) Consider the surfacez=x3-xyand a pointP: (1,2,0) on the surface.a:Find the maximum rate of change of the functionf(x, y) =zat pointP. Also findthe direction that has the maximum rate of change.
b:Find the equations of the tangent plane and normal line to the surface at pointP.
2:(15 Points) Consider the functionf(x, y) = (x2+y2)ex2-y2defined on the discx2+y24. Find theabsolute extremas off.(Hint: Do not use Lagrange multiplier)

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