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The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.

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#### Solution

We know A function f is not differentiable at a point x_{0} belonging to the domain of f if one of the following situations holds

**(i)** f has a vertical tangent at x_{0}

**(ii)** The graph of f comes to a point at x_{0} ......(either a sharp edge ∨ or a sharp peak ∧)

For the given graph f

At x = – 1, a sharp edge ∨

At x = 8, a sharp peak ∧

At x = 4, discontinuity

At x = 11, perpendicular tangent

∴ The given graph is not differentiable at

x = – 1, 8, 4, 11

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