CBSE Class 12 Sample Paper for 2024 Boards

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Question 25 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 8, 2026 by

Check whether the function f:R→R defined by f(x)=x^3+x, has any critical point/s or not ? If yes, then find the point/s

Check whether f(x) = x^3 + x has any critical point/s or not [Video] - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 25 - 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

š‘“(š‘„)=š‘„3+š‘„ Finding š’‡^ā€² (š’™) š‘“ā€²(š‘„)= 3š‘„^2+1 Putting š’‡ā€²(š’™)= 0 to find critical points 3š‘„^2+1 = 0 3š‘„^2=āˆ’1 š’™^šŸ = (āˆ’šŸ)/šŸ‘ x = Ā±āˆš((āˆ’1)/3) x = Ā±āˆš(šŸ/šŸ‘) š’Š So, x is an imaginary number But, given that x is a real number as š‘“:ā„ā†’ā„ Therefore, there is no value of x āˆˆš‘…, when š’‡ā€²(š’™)= 0 Thus, f(x) does not have any critical points

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