# Is #f(x)=e^-xcos(-x)# increasing or decreasing at #x=pi/6#?

##### 1 Answer

Nov 20, 2015

First, note that because the cosine function is and **even function** , then

#### Explanation:

The function will be increasing if the first derivative is positive at

Also note that **ALWAYS positive** regardless what value of x you insert.

Let's find **product rule** ...

Both sine and cosine of **positive number**. And, as stated above,

So, **negative** )

Answer: f(x) is **decreasing** at

hope that helped