Challenging problem, :)
Construct a continuous and differentiable function of real variable that vanishes outside the interval (a,b).
Coment: ofcource it is ment that function do not vanish inside the interval

Question

Challenging problem, :)
Construct a continuous and differentiable function of real variable that vanishes outside the interval (a,b). 
Coment: ofcource it is ment that function do not vanish inside the interval

anonymous · Answer

there are, almost for sure, more then 1 solution. I just wonder what you guys can find and if it would be simmilar to what i got.

experimentx · Answer

can i make use of step function?

anonymous · Answer

no, lol

anonymous · Answer

would be to easy

experimentx · Answer

yeah

anonymous · Answer

What about a uniform probability density function on the interval [a, b]? Or is that cheating? :P

experimentx · Answer

i have seen it though ... somewhere ... like batman equation.

anonymous · Answer

ilustrate me on that, I don't know how the function looks like

anonymous · Answer

@Traxter  i just was looking in wikioedia about this probability function, but it looks to me that it wouldn't be continuous on all R

experimentx · Answer

let's try this
$$ f(x) = \sqrt{x-a} + \sqrt{b-x}$$

anonymous · Answer

but this woud be undefind in Reals outside the interval [a,b]

experimentx · Answer

so you want zero outside that boundary?

anonymous · Answer

yes, :)

anonymous · Answer

it need to be continuos and differentiable in all R

experimentx · Answer

|dw:1347881987604:dw| something like this?

anonymous · Answer

yes, that what i got, :)

experimentx · Answer

not sure ... this would be differentiable at point a and b

anonymous · Answer

yes

experimentx · Answer

you sure ... it is differentiate at point a and b?

anonymous · Answer

|dw:1347882095758:dw|
it is more like this