Midterm 2 Spring 2008 - Math 107 Calculus II Spring 2008...

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Math 107: Calculus II, Spring 2008: Midterm Exam II Solutions1.(a) Ifg(x, y) =e2xcos(y), find(b) The functionf(x, y)has a critical point at(-1,3)and Hessian matrixHf(-1,3) =-522-1.Is this critical point a local max, local min, or saddle point? (Explain your rea-soning.)(c) Which of the following partial derivatives gives the slope of the tangent line aty= 1to thex= 2cross-section off(x, y)? (Circle your answer.)∂f∂x(1,2)∂f∂x(2,1)∂f∂y(1,2)∂f∂y(2,1)2g∂x∂y=-2e2xsin(y)2g∂x ∂y;
(b) To classify this critical point, we find the determinant of the Hessian matrix. This

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