# Is #f(x)=(1-xe^x)/(1-x^2)# increasing or decreasing at #x=2#?

##### 2 Answers

Function

#### Explanation:

To find whether a function is increasing or decreasing at a given point say

As

and at

=

As

graph{(1-xe^x)/(1-x^2) [-9.67, 10.33, -1.12, 8.88]}

Increasing

#### Explanation:

the sign of the derivative of the function determines if its increasing or decreasing

therefore, we have to differentiate it first,

I'll use the quotient rule here

therefore derivative =

therefore, just put in x = 2

this value is positive, therefore

the function is increasing at