SOLUTION: Please help me with this problem: Let f be the function f(x) = {{{xe^(-x^(2))}}} where x is a set of real numbers. Find the critical numbers of f. (It is helpful to note that {{{e

Question 1033806: Please help me with this problem:
Let f be the function f(x) = where x is a set of real numbers. Find the critical numbers of f. (It is helpful to note that is nonzero for any value of x.) Find the intervals on which f is increasing and on which f is decreasing. Use the information found to tell where f attains local maximum and minimum values.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
==> f'(x) = .
Let f'(x) be equal to 0.
==> ==> or , the critical numbers of f(x).
As you mentioned , so no solution comes from this.
In (, ), f'(x) < 0, so f(x) is decreasing there.
In (,), f'(x) > 0, so f(x) is increasing there.
In (,), f'(x) < 0, so f(x) is decreasing there.
Therefore f(x) attains local min at , while it attains a local max at .
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