265f06final

# 265f06final - Iowa State University Math 265 Instructor:...

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Iowa State University Math 265 Final Exam Dec. 14, 2006 Name: Instructor: TA: Section: Instructions: 8 questions. 10 points for each question. Answer each question completely. Show all work. No credit given for mere answers with no work shown. Show the steps of calculations. State the reasons that justify conclusions. 1. Find the equation of the plane through (1 , 2 , 3), (0 , 2 , 8) and ( - 1 , 1 , 6). Equation: 2. Consider the parametric curve C : x ( t ) = t 2 y ( t ) = t 3 , where t is a parameter. Find a unit tangent vector T and a unit normal vector N at the point (4 , 8) on C . T = N =

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Iowa State University Math 265 Final Exam Page 2 3. Find the maximum and minimum values of f ( x,y ) = 2 x 2 - y 2 subject to x 3 + y 3 = 56. maximum = minimum =
Iowa State University Math 265 Final Exam Page 3 4. Suppose f ( x,y,z ) is a diﬀerentiable function at the point (1 , 1 , 1) and ∂f ∂x (1 , 1 , 1) = 2 , ∂f ∂y (1 , 1 , 1) = - 1 , ∂f ∂z (1 , 1 , 1) = 2 (a) Find the directional derivative of

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## 265f06final - Iowa State University Math 265 Instructor:...

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