I have the function $f(x)=(x^2(e^x-1))^{\frac{1}{5}}$ and I would like to determine a qualitative graph of the function in the neighbourhood of $x=0$. I know that there might be an inflection point in $x=0$, so personally, I would most likely calculate the second derivative of the function $f(x)$ in the point $x=0$, but I don't know how to actually determine if there's an inflection point and what kind of inflection it is.
2026-03-23 02:42:54.1774233774
How to determine a qualitative graph of a function in the neighbourhood of a point?
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