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GATE 2024 CS (CS1) – Question 11

Engineering Mathematics · Calculus · 1 mark · Multiple choice

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

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

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Correct answer: (D) $\{-1,0,1\}$

Explanation

$x$ and $x^3$ intersect at -1, 0, 1. The max switches between the two curves with different slopes at each crossing, creating corners at -1, 0, 1.