# How do you find the critical points and the open intervals where the function is increasing and decreasing for #y = xe^(x(2 - 3x))#?

##### 1 Answer

The function is increasing on the interval:

#### Explanation:

Jasivan S, gives an excellent answer to the question asked, but I suspect that the intended question was: Find the open intervals on which the function is increasing and those on which it is decreasing. (Rather than finding those on which it is doing both.)

See Jasivan S. answer to find the derivative:

and the critical numbers:

(I'm used to thinking of critical points as points in the domain, so these would be the critical points. Some think of critical points as points on a graph, in which case, you'd need the

As you probably know, to investigate increasing and decreasing behavior, we consider the sign of

Because

positive on

negative on

Cosequently,

The function is increasing on the interval: