For the function f ( x ) = x 2 x − 1 , why is 1 not a critical point, along with 0 and 2? Don't critical points include discontinuities?

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Mark Rosales

2022-11-19

For the function

f (x) = \frac{x^{2}}{x - 1}

, why is

1

not a critical point, along with

0

and

2

? Don't critical points include discontinuities?

h2a2l1i2morz

Beginner2022-11-20Added 19 answers

The domain of the function is {

x \in R, x \neq 1

}, and thus as

x \in R, x \neq 1

is not in the domain of

f (x)

it cannot be a critical point.
Logically, if a point is not in the domain of a function

f

, it does not exist for

f

, and thus it cannot be a critical point for

f

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