# Is #f(x)=1-x-e^(-3x)/x# concave or convex at #x=4#?

##### 1 Answer

Feb 5, 2018

Let's take some derivatives!

#### Explanation:

For

This simplifies (sort of) to

Therefore

Now let x = 4.

Observe that the exponential is always positive. The numerator of the fraction is negative for all positive values of x. The denominator is positive for positive values of x.

Therefore

Draw your conclusion about concavity.