Let f: R R be a function such that f(x) = \x, x^3\, x ∈ R, where R is the set of all real numbers. The set of all points where f(x) is NOT differentiable is

GATE CSE 2024 Session 1 Q11: Points where max{x, x³} is not differentiable

Engineering Mathematics
1 mark
MCQ
−1/3 if wrong

Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that $f(x) = \max\{x, x^3\}$ , $x \in \mathbb{R}$ , where $\mathbb{R}$ is the set of all real numbers. The set of all points where $f(x)$ is NOT differentiable is

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Answer: D (official GATE 2024 final answer key)

Concept used: The max of two smooth functions has corners where they cross with different slopes.

First step: Solve $x = x^3$ and check the slopes $1$ and $3x^2$ at each crossing.

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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GATE CSE 2024 Session 1 Q11: Points where max{x, x³} is not differentiable

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