# How do you find points of inflection and determine the intervals of concavity given #y=xe^x#?

##### 1 Answer

Feb 15, 2017

Point of inflection is at

#### Explanation:

At points of inflection, second derivative of the function is equal to zero. Hence le us first wok out second derivative for

As

and

=

and this is zero at

As there is only one point of inflection, we have two ranges

In the range

in the range

graph{xe^x [-7.4, 2.6, -1.56, 3.44]}