Laplace's Method

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Laplace's method fits a gaussian to any possible (hard, unnormalized) distribution.

[@GoldenMunkee]

It seems in your example, the mode could also be sqrt(5)?

[@zijianhuang8141]

why x is mode h'(x) is 0?

[@MeerkatStatistics]

The mode is the local maximum of a function. The derivative of a function at the local maximum (or minimum) is 0.