Question

a)Construct a function f(x) that is only differentiate at x =0 and x =1
b) More generally, given a1,.....,an in R distinct. Construct a function g(x) that is differentiable at x = a1, a2, ...., an
Please, help

Answer 1

@perl

Answer 2

you want a function, e.g. that will be continuous over [0,1] but not any farther?
I would think if you just define a function in a couple of ways.

Make up/give it a definition you feel like. (i might be wrong)

Answer 3

@idu
its not differential on an interval see distinsit points 0 and 1
right @OOOPS ?

Answer 4

@idu a function differentiate at a, then it is continuous at a but not vice versa.

Answer 5

sure, tnx for showing:)

Answer 6

@Marki yes, they are distinct points

Answer 7

eh, i need ur help a bit , what topic is it ?

Answer 8

it is called "Diffentiability of function of one variable"

Answer 9

ok wait i'll read about it , i guess i forgot this thing

Answer 10

My prof uses limit approaching.

Answer 11

eh seems i dont understand the question it self :|
straggling

Answer 12

ugh lol ok i misunderstood it need not to be discrete xD
so we can make it continues function

Answer 13

take dirichlet function function and multiply it by x^2(x-1)^2

Answer 14

show me, please

Answer 15

dirichlet function(D(x)) is not continuous anywhere, just show that f(x) = D(x)*x^2(x-1)^2 is differentiable at x = 0 and x = 1 using the limit definition of derivative

Answer 16

@rational so
x^2(x-1)^2 cuz of (x-0)^2(x-1)^2?

Answer 17

http://math.stackexchange.com/questions/108388/function-which-is-continuous-everywhere-in-its-domain-but-differentiable-only-a

Answer 18

@rational thanks for the link.

Answer 19

interesting

Answer 20

Wonder how to graph:
\(f(x) =\begin{cases}x^2~~if~~x\in Q\\0~~if~~x\notin Q\end{cases}\)

Answer 21

feels something like this XD