Function with Always-Zero Derivative Is Constant

Explanations 3

• Suppose a function f(x)f(x)f(x) is continuous on [a,b][a,b][a,b] and differentiable on (a,b)(a,b)(a,b). If f′(x)=0f'(x)=0f′(x)=0 for all xxx in (a,b)(a,b)(a,b), what would that …

  By Steven Kwon, Moor Xu

• Steven Kwon already gave a nice explanation with good intuition. Here we'll give a (nonstandard?) proof avoiding the mean value theorem, inspired by a blog post of Tim Gowers. S…

  By Victor Wang, Moor Xu, Alex Federspiel

• Here is an interesting problem in elementary calculus:(taken from a problem solving group on Facebook.) f:[0,1]→Rf:[0,1]\rightarrow \textbf{R}f:[0,1]→R is continuous on [0,1][0,…

  By Aritro Pathak