Question

What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
​increases, decreases, and is​ constant?
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Part 1
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
​increases? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The open interval is
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
None
Part 2
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
​decreases? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The open​ interval(s) is/are
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
None
Part 3
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x EndFraction
is​ constant? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The open interval is
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
None

Answer 1

f(x) = 1/x ⇒ f'(x) = -1/x^2, which is < 0 for all x ≠ 0.

Part 1 (increasing): B. None.

Part 2 (decreasing): A. (-∞, 0) and (0, ∞).

Part 3 (constant): B. None.