This question is similar to Chapter 5 Class 12 Continuity and Differentiability - Ex 5.1
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CBSE Class 12 Sample Paper for 2025 Boards
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Question 19 [Assertion Reasoning] Important You are here
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CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Oct. 3, 2024 by Teachoo
This question is similar to Chapter 5 Class 12 Continuity and Differentiability - Ex 5.1
Please check the question here
Question 19 Statement A Assertion (A): Consider the function defined as π(π₯)=|π₯|+|π₯β1|,π₯βπ . Then π(π₯) is not differentiable at π=π and π=π. Statement R Reason (R): Suppose π be defined and continuous on (π,π) and πβ(π,π), then π(π₯) is not differentiable at π₯=π if lim_(ββ0^β )β(π(π+β)βπ(π))/ββ lim_(ββ0^+ )β(π(π + β)βπ(π))/β. (A) Both (A) and (R) are true and (R) is the correct explanation of (A). (B) Both (A) and ( π ) are true but (π ) is not the correct explanation of (π΄). (C) (A) is true but (R) is false. (D) (A) is false but (π ) is true.Checking Assertion Assertion (A): Consider the function defined as π(π₯)=|π₯|+|π₯β1|,π₯βπ . Then π(π₯) is not differentiable at π=π and π=π. Given π(π₯)= |π₯|+ |π₯β1|. Here, we have 2 critical points x = 0 and x β 1 = 0 i.e. x = 0, and x = 1 Letβs draw its graph From graph, we can see that At x = 0 and x = 1, It is an edge point And, the function is not differentiable at edge points. Since at x = 0, and x = 1 is not differentiable β΄ Assertion is true Checking Reason Reason (R): Suppose π be defined and continuous on (π,π) and πβ(π,π), then π(π₯) is not differentiable at π₯=π if lim_(ββ0^β )β(π(π+β)βπ(π))/ββ lim_(ββ0^+ )β(π(π + β)βπ(π))/β.. Here, reasoning is describing the differentiability test lim_(ββ0^β )β(π(π+β)βπ(π))/β is Left hand derivative at x = c lim_(ββ0^+ )β(π(π + β)βπ(π))/β is Right hand derivative at x = c And, since the function is not differentiable at x = c, LHD β RHD This is true Hence, Reason is true Is Reason a Correct explanation for Assertion? Since Derivative test can be used to check differentiability at x = 0, and x = 1 Thus, we used the concept mentioned in Reasoning to check Assertion Therefore, Reasoning is a correct explanation for Assertion So, Assertion is true Reasoning is true And, Reasoning is a correct explanation for Assertion So, the correct answer is (a)