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Problem 1 In this problem you will see an example of finding the extreme values of a function of two variables on a bounded region D (including the boundary). Let \(f(x,y) = x^2 - 2xy + 2y\) and D be the region bounded by the triangle whose vertices are (0,0), (0,2), and (3,2). (1) The line segment between (0,0) and (0,2): Let \(g(y) = f(0,y)\) for \(0 \le y \le 2\). Find the absolute extrema of g as you did in differential calculus. Be sure to check the endpoints. (2) The line segment between (0, 2) and (3,2): Let \(h(x) = f(x, 2)\) for \(0 \le x \le 3\). Find the absolute extrema of h. Be sure to check the endpoints. Think about why g(2) and h(0) equal.

          Problem 1 In this problem you will see an example of finding the extreme values of a function of two variables on a bounded region D (including the boundary). Let \(f(x,y) = x^2 - 2xy + 2y\) and D be the region bounded by the triangle whose vertices are (0,0), (0,2), and (3,2).
(1) The line segment between (0,0) and (0,2): Let \(g(y) = f(0,y)\) for \(0 \le y \le 2\). Find the absolute extrema of g as you did in differential calculus. Be sure to check the endpoints.
(2) The line segment between (0, 2) and (3,2): Let \(h(x) = f(x, 2)\) for \(0 \le x \le 3\). Find the absolute extrema of h. Be sure to check the endpoints. Think about why g(2) and h(0) equal.

Problem 1 In this problem you will see an example of finding the extreme values of a function of two variables on a bounded region D (including the boundary). Let f(x,y) = x^2 - 2xy + 2y and D be the region bounded by the triangle whose vertices are (0,0), (0,2), and (3,2).
(1) The line segment between (0,0) and (0,2): Let g(y) = f(0,y) for 0 ≤ y ≤ 2. Find the absolute extrema of g as you did in differential calculus. Be sure to check the endpoints.
(2) The line segment between (0, 2) and (3,2): Let h(x) = f(x, 2) for 0 ≤ x ≤ 3. Find the absolute extrema of h. Be sure to check the endpoints. Think about why g(2) and h(0) equal.

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