Why is this?

[Valentin Albillo]

(04-08-2022 01:40 AM)lrdheat Wrote:  Yes, and this is more intuitive to me. Is it purely coincidental that the max
of x*e^(-x^2) is (sqrt 2)/2, or is there a direct relationship to the sine function? I’m thinking that I am missing some basic math…

- The derivative of y = x * e^(-x^2) is y' = e^(-x^2) * (1 - 2 * x^2)

- To find the extrema of y you must solve y' = 0.

- The exponential term is never 0 and the polynomial term 1 - 2 * x^2 is 0 for x = Sqrt(2) / 2, which is where y has a maximum.

- There's no relationship whatsoever to the sine function, just numerical coincidence with the numerical value of sin(45 deg), that's all.

V.