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 Feb. 10, 2025 by Teachoo

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

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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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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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