Answer:
has no relative extrema when the domain is (the set of all real numbers other than .)
Explanation:
Assume that the domain of is (the set of all real numbers other than .)
Let and denote the first and second derivative of this function at .
Since this domain is an open interval, is a relative extremum of this function if and only if and .
Hence, if it could be shown that for all , one could conclude that it is impossible for to have any relative extrema over this domain- regardless of the value of .
.
Apply the product rule and the power rule to find .
In other words, for all .
Since the numerator of this fraction is a non-zero constant, for all . (To be precise, for all .)
Hence, regardless of the value of , the function would have no relative extrema over the domain .
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