Differentiability query !!

[Anjali]

If f(x)=|x−1|+|x−2|+|x−3|, then f (x) is differentiable at

(a) 0   (b) 1   (c) 2   (d) 3

[mrittik]

f(x)=(x-1)-(x-2)-(x-3)=-x+4, x>1
     =-3x+ 6 x<1

now you can do this easily with 2 & 3 also...so now this is no where differentiable

[Anjali]

Mrittik I have already segregated it into parts ( limit ranging from 1 to 3 ) . But a mod function is not differentiable at 0 . How can we conclude the same result for other options ?

[mrittik]

are baba mod x is differentiable at x that is diff issue...this problem has diff issue...you just make the fns..at 1, 2 & 3...that all

[Granpa Simpson]

The function will be differentiable at x=0..is it the answer..??

[neha:)]

It should be differentiable at 0!

[Granpa Simpson]

Yes it shud be differentiable at x=0..wats the answer anyhow..??

[Homer Simpson]

Anjali, here we are not dealing with mod x, rather a different mod based function. So you need to find the function for different intervals and then see.

[mrittik]

@tsuki...thats my point x>0 OR x>0 is the same fn here....thats why it is differentiable at x=0

[mrittik]

mod x is f(x)=x, x>0    so f'(x)=1 x>0
                    =-x, x<0             =-1 x<0......understood anjali?

[Anjali]

@mrittik , so you mean that we have to form functions and then test LHD and RHD at 1,2 and 3. Is that so ?
And plz have a look at the optimization problem that I have posted :-)

[Akshay Jain]

The function is differentiable at x=0
plot the function at points x=-0.5, 0 nd 0.5
u vl get a straight line => differentiable at x=0

[Anjali]

Thanks Akshay - but is my method correct ?