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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SOLVED:Give an example of a continuous function on an open interval that achieves its extreme values on the interval. Give an example of a continuous function defined on an open interval that does not achieve its extreme values on the interval.
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Consider the function on the interval (0,2 π) . For each function, (a) find the open interval(s) on which the function is increasing or decreasing, (b) apply the First Derivative Test to identify all relative extrema, and (c) use a graphing utility to confirm your results. f(x)=sinx cosx 5 | Numerade
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SOLVED: Find the opon intervalls) on which tho function Increasina and dpcroasing: Identify tne function's local and absolute extreme values, any, saying where they occur:f(x) =x4 18xOn what open interval(s), any; the function increasing? Select the correct choice below and, necessanthe answer box(es complete your choiceThe function increasing on the open intervalls) (Type your answer interval noltation; Use integers or fractions for any numbers Ihe expression Use COmmfseparate answemsaf needed
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