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in Continuity and Differentiability by (49.9k points)
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Let f(x) = {((2 - x), when x ≥ 1), (x, when 0 ≤ x ≤ 1). Show that f(x) is continuous but not differentiable at x = 1.

1 Answer

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Best answer

Consider left hand limit at x = 1

So we get

Here Lf' = Rf'

Therefore, the function is continuous but not differentiable at x = 1.

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