Question

Problem 1 (25 points) A. Find the total differential of U = (x1 - x2) / 2x1^2 (present the computational steps in a neat and structured manner) (4 points). B. Find the extremum values of y = f(x1, x2) = x1^3/3 + x1x2 + x2^2 (present the computational steps in a neat and structured manner) (8 points). C. Find the critical values of the function: y = x + 1/x (with x ? 0) and compare the "minimum" value with the "maximum" value (present the computational steps in a neat and structured manner) (5 points). How can you explain your result (3 points)? D. Consider the following function: F(w, x, y) = x^2 + 3xy + 2yw + y^2 + w^2 - 11 = 0. Show that an implicit function w = g(x, y) is defined around point P (x = 1, y = 2, w = 0) (present your answer in a neat and structured manner) (3 points). Find ?w/?x and evaluate it at point P (2 points).

          Problem 1 (25 points)

A. Find the total differential of U = (x1 - x2) / 2x1^2 (present the computational steps in a neat and structured manner) (4 points).

B. Find the extremum values of y = f(x1, x2) = x1^3/3 + x1x2 + x2^2 (present the computational steps in a neat and structured manner) (8 points).

C. Find the critical values of the function: y = x + 1/x (with x ? 0) and compare the "minimum" value with the "maximum" value (present the computational steps in a neat and structured manner) (5 points). How can you explain your result (3 points)?

D. Consider the following function: F(w, x, y) = x^2 + 3xy + 2yw + y^2 + w^2 - 11 = 0. Show that an implicit function w = g(x, y) is defined around point P (x = 1, y = 2, w = 0) (present your answer in a neat and structured manner) (3 points). Find ?w/?x and evaluate it at point P (2 points).

Problem 1 (25 points)

A. Find the total differential of U = (x1 - x2) / 2x1^2 (present the computational steps in a neat and structured manner) (4 points).

B. Find the extremum values of y = f(x1, x2) = x1^3/3 + x1x2 + x2^2 (present the computational steps in a neat and structured manner) (8 points).

C. Find the critical values of the function: y = x + 1/x (with x ? 0) and compare the "minimum" value with the "maximum" value (present the computational steps in a neat and structured manner) (5 points). How can you explain your result (3 points)?

D. Consider the following function: F(w, x, y) = x^2 + 3xy + 2yw + y^2 + w^2 - 11 = 0. Show that an implicit function w = g(x, y) is defined around point P (x = 1, y = 2, w = 0) (present your answer in a neat and structured manner) (3 points). Find ?w/?x and evaluate it at point P (2 points).

Added by Carolina S.

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