A Function ?

Calculus Level 3

Does there exist a function defined on the reals which is differentiable at only one point?

Yes This Question Does Not Make Sense No Impossible to Say

Christopher Criscitiello by Christopher Criscitiello , 25, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Arjen Vreugdenhil
Dec 20, 2017

An example of such a function is f ( x ) = { x 2 if x is rational , 0 if x is irrational f(x) = \begin{cases} x^2 & \text{if}\ x\ \text{is rational}, \\ 0 & \text{if}\ x\ \text{is irrational}\end{cases}

It is continuous only at x = 0 x = 0 ; its derivative there is f ′ ( x ) = 0 f'(x) = 0 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...