Find the open intervals on which the function $f(…
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Discuss the extreme-value behavior of the function $f(x)=$ $x \sin (1 / x), x \neq 0 .$ How many critical points does this function have? Where are they located on the $x$ -axis? Does $f$ have an absolute minimum? An absolute maximum? (See Exercise 49 in Section $2.3 .$ .