Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

If a function has it`s first partial derivatives continuous then if on this curve we fix two distinct points and let them join by a secant line then we know that when these point begin to approach each other then the portion of the curve between these two point is the same line as their secant when these two points are in a differential part of curve.But even in this differential part there are still infinite number of points.So should we conclude that tangent on such kind of curve (defined by a function of at least first order continuous derivative) touches more than one point of the curve?

share|cite|improve this question
What do you mean by a differential domain? – Espen Nielsen Nov 25 '12 at 17:37
It was intended to make realization of a differential part of the curve in which the points lie. – Abhinav Anand Nov 25 '12 at 17:50
up vote 0 down vote accepted

No, because the tangent is defined as the limit of the secant through two point as the two points approach each other. The concept of limit is often not easy to grasp, and a study of its historical development will show you why.

share|cite|improve this answer
Elaborate your more. – Abhinav Anand Nov 26 '12 at 13:51

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.