#### Provide Solution For R.D.Sharma Maths Class 12 Chapter 9 Differentiability Exercise 9.2 Question 8 Maths Textbook Solution.

Answer: $f\left ( x \right )=|x-2|+|x-3|+|x-4|+|x-5|+|x-6|$

Hint: Modulus function f(x) = $|x|$ is continuous but not differentiable at x = 2,3,4,5,6

Given: To write a function which is everywhere continuous but fails differentiability exactly at five points.

Solution:

We know that, polynomial functions are always continuous and differentiable.

Let us consider, $f\left ( x \right )=|x|$

Modulus functions are always continuous.

So, $|x|$  is continuous.

Now, there is more than one slope possible. So it is not differentiable as we know that

Using mod function, we can write the function which is non-derivable at exactly 5 points and continuous always is

$f\left ( x \right )=|x-2|+|x-3|+|x-4|+|x-5|+|x-6|$
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