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Solution

**Solution:** Non-differentiable points occur where expressions inside modulus = 0. 1. $2x + 1 = 0 \Rightarrow x = -\dfrac{1}{2}$ 2. $x + 2 = 0 \Rightarrow x = -2$ 3. $x^2 + x - 2 = 0 \Rightarrow x = 1, -2$ Unique points: $x = -2, -\dfrac{1}{2}, 1$ Hence, number of non-differentiable points = 3. $\boxed{\text{Answer: (B) 3}}$

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Solution

$f(x) = x^{1/3}$ is continuous at $x = 0$ but derivative $\dfrac{df}{dx} = \dfrac{1}{3}x^{-2/3}$ is not defined at $x = 0.$ Hence, function is continuous but not differentiable at 0.

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Solution

Each $|x|$ term is non-differentiable at the point where its argument = 0. Points: $x = 0, -1, 4$.

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Solution

$x=x^3$ → $x=0,\pm1$.