consider the function ( f(x)=\frac{x - 4}{x + 2} ).\nis ( x=-2 ) a critical number of ( f )?\nyes\nno\nwhy…

consider the function ( f(x)=\frac{x - 4}{x + 2} ).\nis ( x=-2 ) a critical number of ( f )?\nyes\nno\nwhy or why not?\nthe function is not defined at ( x=-2 ).\nthe function is differentiable at ( x=-2 ).\nthe function is not differentiable at ( x=-2 ).\nthe function is defined at ( x=-2 ).

consider the function ( f(x)=\frac{x - 4}{x + 2} ).\nis ( x=-2 ) a critical number of ( f )?\nyes\nno\nwhy or why not?\nthe function is not defined at ( x=-2 ).\nthe function is differentiable at ( x=-2 ).\nthe function is not differentiable at ( x=-2 ).\nthe function is defined at ( x=-2 ).

Answer

Explanation:

Step1: Recall the definition of critical number

A critical number of a function (y = f(x)) is a number (c) in the domain of (f) such that (f^{\prime}(c)=0) or (f^{\prime}(c)) does not exist.

Step2: Check the domain of (f(x)=\frac{x - 4}{x + 2})

The function (f(x)=\frac{x - 4}{x + 2}) is a rational function. The denominator (x + 2=0) when (x=-2). So the domain of (f(x)) is ({x|x\neq - 2}). Since (x =-2) is not in the domain of (f(x)), it cannot be a critical number.

Answer:

No. The function is not defined at (x=-2).