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Question
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 x0 belonging to the domain of f if one of the following situations holds
(i) f has a vertical tangent at x0
(ii) The graph of f comes to a point at x0 ......(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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