Let If and denote the number of points where is not continuous and not differentiable respectively, then is equal to [2024]

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Solution

Q.
Let $f (x) = | 2 x^{2} + 5 | x | - 3 |, x \in R .$ If $m$ and $n$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $m + n$ is equal to [2024]

1 5

2 3

3 2

4 0

Ans.
(2)

We have, $f (x) = | 2 x^{2} + 5 | x | - 3 |, x \in R$

$f (x)$ is continuous at every point.

So, $m = 0$

Now, from the graph, $f (x)$ is non-differentiable at $x = - \frac{1}{2}, 0, \frac{1}{2}$

So, $n = 3$

$∴$ $m + n = 3$

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