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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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.