The number of points at which the function fx - maxa - x- a - x- b- - - x - - 0 - a - b cannot be differentiable is-are

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The number of...

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The number of points at which the function $f (x) = max {a - x, a + x, b}, - \infty < x < \infty, 0 < a < b$ cannot be differentiable is/are

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f (x) = | 2 x + 1 | - 3 | x + 2 | + | x^{2} + x - 2 |, x \in R

The set of all points, where the function $f (x) = \frac{x}{1 + | x |}$ is differentiable, is

f (x) = e^{x}

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} - 2 sin x, & - π \leq x \leq \frac{- π}{2} a cos (x) + b, & \frac{- π}{2} < x < 0 - 2 + cos x, & 0 \leq x \leq \frac{π}{2} c sin x, & \frac{π}{2} < x \leq π \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

[- π, π],

f (x)

a

b

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{sin x}{x} & - 2 \leq x < 0 a \cdot 2^{x} & 0 \leq x \leq 1 b + x & 1 < x \leq 2 \end{matrix}

[- 2, 2]

f (x) = | x |, g (x) = | x |^{2}

h (x) = | x |^{3}

x = 0

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