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Let f: R → R be a function such that f(x) = max{x, x³}, x ∈ R, where R is the set of all real numbers. The set of all points where f(x) is NOT differentiable is

1. {-1,1,2}
2. {-2,-1,1}
3. {0,1}
4. {-1,0,1}

Correct answer: {-1,0,1}

Solution

The function f(x) = max{x, x³} is not differentiable at points where the two expressions x and x³ intersect or change dominance, which occurs at x = -1, 0, and 1. At these points, the left-hand and right-hand derivatives do not match, indicating non-differentiability.

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