what is the largest open interval over which f(x) = \\frac{1}{x} increases, decreases, and is…

what is the largest open interval over which f(x) = \\frac{1}{x} increases, decreases, and is constant?\nwhat is the largest open interval over which f(x) = \\frac{1}{x} increases? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the open interval is \n(type your answer in interval notation. use a comma to separate answers as needed.)\nb. none

what is the largest open interval over which f(x) = \\frac{1}{x} increases, decreases, and is constant?\nwhat is the largest open interval over which f(x) = \\frac{1}{x} increases? select the correct choice below and, if necessary, fill in the answer box to complete your choice.\na. the open interval is \n(type your answer in interval notation. use a comma to separate answers as needed.)\nb. none

Answer

Explanation:

Step1: Find the derivative

The function is $f(x)=\frac{1}{x}=x^{-1}$. Using the power - rule $(x^n)^\prime=nx^{n - 1}$, the derivative $f^\prime(x)=-x^{-2}=-\frac{1}{x^{2}}$.

Step2: Analyze where the function increases

A function $y = f(x)$ increases when $f^\prime(x)>0$. But $f^\prime(x)=-\frac{1}{x^{2}}<0$ for all $x\neq0$. So the function $f(x)=\frac{1}{x}$ does not increase on any open interval.

Answer:

B. None