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Let f(x) = x^2/2, 0 ≤ x < 1 f(x) = 2x^2 - 3x + 3/2, 1 ≤ x ≤ 2

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Let f(x) = x2/2, 0 ≤ x < 1

f(x) = 2x2 - 3x + 3/2, 1 ≤ x ≤ 2

Discuss the continuity of f , f' and f" on [0, 2].

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Clearly, RHL (at x = 1) = 1/2

and LHL (at x = 1) = 1/2

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