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Show that the function f(x)=|x| is …

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Show that the function f(x)=|x| is not differentiable at x=0

Posted by Mallikarjun Patil 4 years, 10 months ago

CBSE > Class 12 > Mathematics

1 answers

Gaurav Seth 4 years, 10 months ago

Given values :

The function f(x) = x is continuous at x = 0.

To Prove :

That the function f(x)=x is continuous at x=0, but not differentiable at

x = 0.

Solution :

First of all prove :

We know that :

Note :

If this is required then use!

Then,

So,

Now,

To Represent :

So,

Did you observe?

So, You should obesreve! that,

The limit from the right is 1 while the limit from the left is - 1.

Hence,

The two sided limit does not exist.

That is, the derivative does not exist at x = 0

0Thank You

ANSWER

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