Talk:Critical point (mathematics)/Comments

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This is a fundamental topic, but the current brief treatment is confused, and distracted by side issues. A critical point is a point where the derivative fails to be surjective. This is a subtle concept which needs to be introduced through examples. Geometry guy 00:40, 21 May 2007 (UTC)

I don't agree with this.

First, the definition should not use words like "surjective" as they are not needed. Second, the definition is that a critical value of a real-valued function of a real variable, f, is a number c in the domain of f at which the derivative, f'(x), is zero or undefined. Third, the value is the domain element, and the critical point is the associated (x,y). The existing article has this wrong.

Dr. Mike DrMWEcker (talk) 04:13, 9 April 2008 (UTC)