0

Is every function whose derivative exists at a point differentiable? And, if a function is differentiable does it mean that the derivative is continous?

Gerry Myerson
  • 179,216
Thewhy
  • 1
  • Are you talking about single-variable functions or multi-variable functions? – Guy Jun 11 '16 at 06:13
  • Hint: for the first question consider a function that is zero everwhere except on the interval $(0,1)$, where it is has the value one; i.e $\chi_{(0,1)}$. For the second question consider the function that is defined to be $x^2sin(1/x)$ everywhere except $x=0$ and, and 0 at $x=0$. – SquirtleSquad Jun 11 '16 at 06:48
  • @Merlinsbeard this should be an answer. – Funktorality Jun 11 '16 at 07:21
  • 1
    Duplicate of: http://math.stackexchange.com/questions/292275/discontinuous-derivative and http://math.stackexchange.com/questions/292275/discontinuous-derivative – MathematicsStudent1122 Jun 11 '16 at 07:55

0 Answers0