Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201910 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
10 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Continuity and Differentiability

JEE Main 2019 · 10 January · Morning Shift · Mathematics · Continuity and Differentiability

Let f(x) = \ cases max(|x|, x ^ 2 ), & |x| ≤ 2 8 - 2|x|, & 2 < |x|...

Let f\left(x\right) = \left\{\begin{cases}max\left(\left|x\right|, {x}^{2}\right), & \left|x\right| \le 2 \\ 8 - 2\left|x\right|, & 2 < \left|x\right| \le 4\end{cases}.\right) LetSbethesetofpointsintheinterval(−4,4)be the set of points in the interval \left(- 4, 4\right) at which ff is not differentiable. Then $SLet f(x) = \ cases max(|x|, x ^ 2 ), & |x| ≤ 2 8 - 2|x|, & 2 < |x| ≤ 4 cases .) Let S be the set of points in the

Options

  1. Aequals {−2,−1,0,1,2}\left\{- 2, - 1, 0, 1, 2\right\}
  2. Bequals {−2,2}\left\{- 2, 2\right\}
  3. Cis an empty set
  4. Dequal {−2,−1,1,2}\left\{- 2, - 1, 1, 2\right\}

Correct answer

A. equals {−2,−1,0,1,2}\left\{- 2, - 1, 0, 1, 2\right\}

Step-by-step solution

Given function is f\left(x\right) = \left\{\begin{cases}max\left(\left|x\right|, {x}^{2}\right), & \left|x\right| \le 2 \\ 8 - 2\left|x\right|, & 2 < \left|x\right| \le 4\end{cases}\right)</p><p>The graph of the function, is</p><p><img alt="" src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/0586fe52-962a-400c-b729-b64749754feb-139.png" style="width: 350px; height: 210px;" /></p><p>We know that, a function is not differentiable at a point where its graph has a sharp corner.</p><p>And, from the graph we can easily conclude thatf(x)\left(x\right) is non-derivable at x=−2,−1,0,1,2x = - 2, - 1, 0, 1, 2

Hence, the set S={−2,−1,0,1,2}.S = \left\{- 2, - 1, 0, 1, 2\right\} .

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

Let ℝ denote the set of all real numbers. Let f : ℝ arrow ℝ be an arbitrary function and… JEE Advanced 2026Consider the function f : (-(π)/(2), (π)/(2)) arrow (-∞, ∞) defined by f(x) = (|x| + |x… JEE Advanced 2026For a real number α , let [α] denote the greatest integer less than or equal to α . For a… JEE Advanced 2026For the function f(x) = e^ |x| - |x| , x ∈ ℝ , consider the following statements… JEE Main 2026Let f(x) = cases (1)/(3), & x ≤ π/2 (b(1- x))/((π-2x)^2), & x > π/2 cases . If f is… JEE Main 2026Let f(x) = cases x^3 + 8 ; & x Then the number of points, where the function g ∘ f is… JEE Main 2026Let f(x)= cases e^ x-1 , & x<0 x^2-5x+6, & x ≥ 0 cases and g(x)=f(|x|)+|f(x)| . If the… JEE Main 2026The number of points, at which the function f(x) = \ 6x, 2 + 3x^2\ + |x - 1|| |x^2… JEE Main 2026The number of points in the interval [2, 4] , at which the function f(x) = [x^2 - x… JEE Main 2026Let f(x)= _ θ arrow 0 ( π x-x^ ((2)/(θ)) (x-1) 1+x^ ((2)/(θ)) (x-1) ), x ∈ R . Consider… JEE Main 2026Let [t] denote the greatest integer less than or equal to t . If the function f(x)=\… JEE Main 2026If the function f(x)= e^ x (e^ x-x -1)+ _ e ( x+ x)-x x-x is continuous at x=0 , then the… JEE Main 2026Let α, β ∈ ℝ be such that the function f(x)= cases 2 α(x^ 2 -2)+2 β x &, x be… JEE Main 2026If f(x)=\ array cc a|x|+x^ 2 -2( |x|)( |x|) x &, x ≠ 0 b &, x=0 array . is continuous at… JEE Main 2026Let f(x)= cases a x^ 2 +2 a x+3 4 x^ 2 +4 x-3 &, x ≠-(3)/(2), (1)/(2) ~b &, x=-(3)/(2)… JEE Main 2026Let [·] denote the greatest integer function, and let f(x)= \ 2 x, x^ 2 \ . Let S = \ x… JEE Main 2026 Full Continuity and Differentiability list Continuity and Differentiability JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs