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Answered question

2022-09-24

what the isolated critical point?

Answer & Explanation

Adelaide Barr

Beginner2022-09-25Added 9 answers

The set of critical points of a function

f : A \to B

is

C P (f) = {x \in A ∣ d f_{x} is not surjective},

where

d f_{x}

denotes the derivative of

f

at the point

x

. A point

x

is an isolated critical point of

f

if there exists

δ > 0

such that

C P (f) \cap {y \in A s.t. | x - y | < δ} = {x} .

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