Question

Monotonicity of a function at a point is discussed only in the neighborhood of the point.

• A. True
• B. False

Answer 1

The correct option is A

True

Earlier we were discussing the monotonicity of a function throughout its domain, meaning if a function is continuously increasing throughout its domain then only the function will be a monotonically increasing function. But if we are discussing the monotonicity of a function about a point then we are just considering the neighborhood of the point forgetting the rest of the domain. So if we are discussing the monotonicity of a function at a point a , then we have to consider three points which are a-h, a, a+h where h is an infinitesimally small positive number.