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Consider the function f : (0, 2) → R defined by f(x) = x 2 2 x + and the function g(x) defined by g(x) = ⎪ ⎩ ⎪ ⎨ ⎧ < < + ≤ < ≤ < 2 x 1 , x 2 3 1 x 0 and x t 0 )}, t ( f min{ . Then,

1. g is not continuous for all x ∈ (0, 2)
2. g is continuous and differentiable for all x ∈ (0, 2)
3. g is continuous but not differentiable at x = 1
4. g is neither continuos nor differentiable at x = 1

Correct answer: g is continuous but not differentiable at x = 1

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