This question is similar to Chapter 5 Class 12 Continuity and Differentiability - Ex 5.1
Please check the question here




CBSE Class 12 Sample Paper for 2025 Boards
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Dec. 13, 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)