F(x)=|x-8|+3
Where is the function decreasing and increasing?
In interval notation?

Question

F(x)=|x-8|+3 
Where is the function decreasing and increasing?
In interval notation?

campbell_st · Answer

graph the function.... makes it easy to see where its increasing and decreasing

use a table of values like

x: 6  : 7  : 8  : 9  : 10
y:

anonymous · Answer

I graphed it on my calc, but what I'm really struggling on is writing the answer in interval notation. Would it be decreasing on (-infinity,8) and increasing on (8,infinity)

anonymous · Answer

? @campbell_st

campbell_st · Answer

thats correct

anonymous · Answer

$$f(x)=|x-8|+3=\begin{cases}x-8+3&\text{for }x\ge8\-x+8+3&\text{for }x<8\end{cases}=\begin{cases}x-5&\text{for }x\ge8\11-x&\text{for }x<8\end{cases}$$
So you have
$$f'(x)=\begin{cases}1&\text{for }x>8\DNE&\text{for }x=8\-1&\text{for }x<8\end{cases}$$
Applying the first derivative test is less tedious, imo. You immediately see on which intervals the function is increasing/decreasing.

anonymous · Answer

...but if you haven't had calculus yet, stick to campbell's method :)

anonymous · Answer

Thank you to both of you! :)