Question 17 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at February 10, 2025 by Teachoo

The set of all points where the function f(x)=x+|x| is differentiable, is

(a) (0,∞) (b) (-∞,0)

(c) (-∞,0)∪(0,∞) (d) (-∞,∞)

This question is similar to Question-15 NCERT-Exemplar-MCQs

The set of all points where function f(x) = x + |x| is differentiable - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 17 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 17 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

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Transcript

𝑓(𝑥) = 𝑥+|𝑥| = {█(𝑥+𝑥, 𝑥≥0@𝑥−𝑥, 𝑥 <0)┤ = {█(2𝑥, 𝑥≥0@0, 𝑥<0)┤ Now, f(x) is a differentiable at x = 0 if LHD = RHD (𝒍𝒊𝒎)┬(𝐡→𝟎) (𝒇(𝒙) − 𝒇(𝒙 − 𝒉))/𝒉 = (𝑙𝑖𝑚)┬(h→0) (𝑓(0) − 𝑓(0 − ℎ))/ℎ = (𝒍𝒊𝒎)┬(𝐡→𝟎) (𝒇(𝟎) − 𝒇(−𝒉))/𝒉 =(𝑙𝑖𝑚)┬(ℎ→0) (2(0) − 0)/ℎ = (𝑙𝑖𝑚)┬(h→0) 0/ℎ = 𝟎 (𝒍𝒊𝒎)┬(𝐡→𝟎) (𝒇(𝒙 + 𝒉) − 𝒇(𝒙 ))/𝒉 = (𝑙𝑖𝑚)┬(h→0) (𝑓(0 + ℎ) − 𝑓(0))/ℎ = (𝒍𝒊𝒎)┬(𝐡→𝟎) (𝒇(𝒉) − 𝒇(𝟎))/𝒉 = (𝑙𝑖𝑚)┬(h→0) (2ℎ − 0)/ℎ = (𝑙𝑖𝑚)┬(h→0) 2ℎ/ℎ = 𝟐 Hence, we can say that f(x) is differentiable on R − {𝟎} or (−∞,𝟎)∪(𝟎,∞) So, the correct answer is (c)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

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