If the domain of a function can be broken into infinite number

if-the-domain-of-a-function-can-be-broken-into-infinite-number

If the domain of a function can be broken into infinite number of disjoint subsets such that every subset has a Rolles point then the function cannot be in a polynomial structure.

A. True

B. False

This question was addressed to me during a job interview.

I’d like to ask this question from Rolle’s Theorem in portion Differential Calculus of Engineering Mathematics

The correct answer is B. False

Easiest explanation: The function could be an infinite degree polynomial (similar to Taylor series), such that after differentiating once we get another polynomial with infinite degree.

Hence, we may conclude that it has infinite distinct roots (with proper choice of polynomial) and hence, the domain can be broken into epsilon (very small) intervals around the roots of the differentiated polynomial to get infinite intervals containing the Rolles point.