Number of points where the function f(x) = (x | vedclass

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(C) The function is $f(x) = (x^2 - 1) |(x - 2)(x + 1)| + \sin(|x|)$.First,analyze the points where the absolute value expressions are zero: $x = 2, -1

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$2$

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(C) The function is $f(x) = (x^2 - 1) |(x - 2)(x + 1)| + \sin(|x|)$.First,analyze the points where the absolute value expressions are zero: $x = 2, -1, 0$.$1$. At $x = 2$: $f(x) = (x^2 - 1) |x - 2| |x + 1| + \sin(|x|)$. Since $|x - 2|$ is not differentiable at $x = 2$ and the other terms are non-zero at $x = 2$,$f(x)$ is not differentiable at $x = 2$.$2$. At $x = -1$: $f(x) = (x^2 - 1) |x - 2| |x + 1| + \sin(|x|) = (x - 1)(x + 1) |x - 2| |x + 1| + \sin(|x|) = (x - 1) |x - 2| (x + 1) |x + 1| + \sin(|x|)$. Since $(x + 1) |x + 1|$ is differentiable at $x = -1$,the product is differentiable at $x = -1$.$3$. At $x = 0$: The term $\sin(|x|)$ is not differentiable at $x = 0$ because the left-hand derivative is $-\cos(0) = -1$ and the right-hand derivative is $\cos(0) = 1$. The other part $(x^2 - 1) |x^2 - x - 2|$ is differentiable at $x = 0$. Thus,$f(x)$ is not differentiable at $x = 0$.Therefore,the function is not differentiable at $x = 0$ and $x = 2$. The total number of points is $2$.

Number of points where the function $f(x) = (x^2 - 1) | x^2 - x - 2 | + \sin(|x|)$ is not differentiable,is

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