Does the converse of Rolle's Theorem hold true? Let [math]f[/math] be continuous on [math][a,b][/math] and differentiable on [math](a,b)[/math]. If there exists [math]c[/math] in [math](a,b)[/math] such that [math]f'(c)=0[/math], does it follow that ...
Does the converse of Rolle's Theorem hold true? Let [math]f[/math] be continuous on [math][a,b][/math] and differentiable on [math](a,b)[/math]. If there exists [math]c[/math] in [math](a,b)[/math] such that [math]f'(c)=0[/math], does it follow that ...
![partial differential equations - Why does $w=u-h$ satisfy mean value property on any ball inside $B$? - Mathematics Stack Exchange partial differential equations - Why does $w=u-h$ satisfy mean value property on any ball inside $B$? - Mathematics Stack Exchange](https://i.stack.imgur.com/0xfxn.png)