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If you are given the function [tex] y = x - 3e^-x^2 [/tex] and you want to find the intervals where the function is increasing and decreasing, concavity, inflection points and any local extreme values, would I first find the derivative?

My work

If [tex] f(x) = x - 3e^-x^2 [/tex] then [tex] f'(x) = 1+6e^(-x^2)xln(e) [/tex[. Then I set this equal to 0 But I get [tex] {e = e, x = RootOf(`.`(1+6*exp(-ln(e)_Z^2)_Zln(e) = 0, _Z))} [/tex]

How would you determine concavity and any local extrema? I know that to get inflection points you take the second derivative and set it equal to 0.

Thanks a lot

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# Homework Help: Increasing and Decreasing Intervals

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