MATHS 2 Marks Questions

f(x) = |log |x||
Since, it is an absolute function. So, it is continuous function. The graph of the function is as below:-

From the graph, it is clear that f(x) is not differentiable at x = -1, 1 but continuous for all x.

Yes, every differentiable function is continuous.

We know that, modulus functionf(x) = |x| is continuous but not differntiable at x = 0.
So,
f(x) = |x| + |x - 1| + |x - 2| + |x - 3| + |x - 4| is continuous but not differentiable x = 0, 1, 2, 3, 4.

No, function may be continuous at a point but may not be differentiable at that point .
For example: function f(x) = |x| is continuous at x = 0 but it is not differentiable at x = 0.

Here,
f(x) = |log |x||
f(x) will always positive and let two points x = 1 and x = -1
f(x) = 0
The function f(x) = |log |x|| is not differentiable at x = -1 and 1.