Question

What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x squared EndFraction
​increases, decreases, and is​ constant?
Question content area bottom
Part 1
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x squared 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.)
B.
None
Part 2
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x squared EndFraction
​decreases? 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.)
B.
None
Part 3
What is the largest open interval over which f left parenthesis x right parenthesis equals StartFraction 1 Over x squared 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^2, f'(x) = -2/x^3.

- f' > 0 for x < 0, so f increases on (-∞, 0).
- f' < 0 for x > 0, so f decreases on (0, ∞).
- f' = 0 nowhere, so f is never constant on any open interval.

Answers:
Part 1: (-∞, 0)
Part 2: (0, ∞)
Part 3: None