Generally speaking, how do I find the point of inflexion of a curve y=f(x) if there is no x such that y'=0.(adsbygoogle = window.adsbygoogle || []).push({});

For example, say we have the curve y=arcsinh(x+1) and want to find its point of inflexion, so y'=1/[1+sqrt{1+(x+1)^2}]=0, but there are no values of x that do that. I tried to use the inverse of x and find dx/dy instead, then set it to zero, but again, I couldn't find a suitable value for y.

How do I approach questions like this?

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# Points of inflexion

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