很容易证明 y=x^x 有极值点x=1/e.

y=x^x
y ' = (ln x + 1)x ^x

y’=0èx=1/e.  y=x^x reaches the minmum at x=1/e. y’ can take any positive number x and the first derivative is negative before reches the minmum at x=1/e and positive after reaches the minmum.