# How do you find the intervals of increasing and decreasing using the first derivative given #y=abs(x+4)-1#?

##### 2 Answers

Increasing when

#### Explanation:

Let's first rewrite this function as a piece wise one.

We have:

Now, we try to find the derivatives for each case. We therefore have:

This really tells us that whenever

Similarly, whenever

We can see that when we graph this:

graph{abs(x+4)-1 [-10, 10, -5, 5]}

We can see that there is a "break" at

And we can see that the line goes downward to the left of

#### Explanation:

- If
#x+4>0# #<=># #x># #-4# then

and

- If
#x+4<0# #<=># #x<# #-4# then

and

Therefore,

&

so