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

##### 1 Answer

#### Explanation:

A function is increasing or decreasing at a given point if its first derivative, evaluated at that point, is positive or negative respectively.

To answer, then, we first must find the derivative of

First, let's use the quotient rule to evaluate the derivative:

Next, we evaluate the first derivative at

Finally, we check the sign of the result.

thus, as the quotient of a positive number and a negative number is negative,

meaning