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