Extremal values/asymptotes

6. Consider the function $f(x) = (e^{?2x})/(2x)$ defined in all of R. Find and classify the extremal values of f. Does f have any asymptotes? If so, find them.

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  • Please leave a comment if you need any clarifications.

  • When evaluating the dobble derivative it seem like you are leaving the (-) out before 2 which i believe gives 2e greater than 0 instead of -2e less than zero. If so, wouldn't it be a global max then?

  • No, I doubled checked my computations and there seems to be no mistake. I also graphed the function, and the critical point is indeed a maximum point.

  • Perfect, thank you so much. I believe i forgot that (2x)^-2 equals 1/4x^2

The answer is accepted.