anonymous
  • anonymous
F(x)=|x-8|+3 Where is the function decreasing and increasing? In interval notation?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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campbell_st
  • campbell_st
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
  • anonymous
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
  • anonymous
? @campbell_st

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campbell_st
  • campbell_st
thats correct
anonymous
  • anonymous
\[f(x)=|x-8|+3=\begin{cases}x-8+3&\text{for }x\ge8\\-x+8+3&\text{for }x<8\end{cases}=\begin{cases}x-5&\text{for }x\ge8\\11-x&\text{for }x<8\end{cases}\] 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
  • anonymous
...but if you haven't had calculus yet, stick to campbell's method :)
anonymous
  • anonymous
Thank you to both of you! :)

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