Find the monotone interval, extreme value, concave-convex interval and inflection point of the function y=xe to the x power by tabular method

Y' = e x (1+x), because e x is always greater than 0, from y'=0, we can get x=- 1.

x & lt- 1，y '

X>- 1, y'>0, so the function interval (-1, inf) is added.

When x=- 1, y'=0, so the minimum value-1/e can be obtained.

Y'' = e x (2+x), when x

When x & gt-2, y''>0, the function is concave in the interval (-2, inf).

On both sides of x=-2, y'' changes sign, so the inflection point is (-2, -2/e 2).