Fundamental Theorem of Calculus properties

[am100181]

Homework Statement

Find a function f : [-1,1] ---> R such that f satisfies the following properties:

a) f is continuous
b) f is restricted to (-1,1) is differentiable
c) its derivative f' is not differentiable on (-1,1)

Homework Equations

The Attempt at a Solution

I kinda think that the mean value theorem and Theorem 2 of the fundamentals $$\int$$f(x)dx = F(b)-F(a) got some link but I can't seem to get it. I do understand that for f'' not to exist, x should be undefined on the (-1,1). Please help.

 

[am100181]

A read somewhere that a hint would be to begin with an absolute value and use $$\int$$f(x)dx = F(b)-F(a) (fundamental theorem of calc prep 2) repeatedly.. but still puzzled

 

[Dick]

Start with c). Pick a nondifferentiable function on (-1,1) and integrate it to get f.

 

[HallsofIvy]

|x| is a very simple function that is not differentiable at x= 0.

 

[sutupidmath]

|x| is a very simple function that is not differentiable at x= 0.

You are right, but the OP is looking for a function such that it is once differentiable on (-1,1) but not twice, and is continuous of course on the same interval.

Edit: ignore it!

 

[HallsofIvy]

Yes, and combining |x| with Dick's suggestion gives exactly that!

(Edit: Too late! I gotcha!)