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 14, 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

𝑓(𝑥)=𝑥3+𝑥 Finding 𝒇^′ (𝒙) 𝑓′(𝑥)= 3𝑥^2+1 Putting 𝒇′(𝒙)= 0 to find critical points 3𝑥^2+1 = 0 3𝑥^2=−1 𝒙^𝟐 = (−𝟏)/𝟑 x = ±√((−1)/3) x = ±√(𝟏/𝟑) 𝒊 So, x is an imaginary number But, given that x is a real number as 𝑓:ℝ→ℝ Therefore, there is no value of x ∈𝑅, when 𝒇′(𝒙)= 0 Thus, f(x) does not have any critical points

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