Extreme value theorem
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To find the extreme values of a function f(x, y) on a curve x=x(t), y=y(t), we treat f as a function of the single variable t and use the Chain Rule to find where d f / d t is zero. As in any other single-variable case, the extreme values of f are then found among the values at the a. critical points (points where d f / d t is zero or fails to exist), and b. endpoints of the parameter domain. Find the absolute maximum and minimum values of the following functions on the given curves. Functions:
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