Check sibling questions

Ex 6.2, 11 - Prove f(x) = x2-x+1 is neither strictly increasing

Ex 6.2,11 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.2,11 - Chapter 6 Class 12 Application of Derivatives - Part 3


Transcript

Ex 6.2, 11 Prove that the function f given by f (𝑥) = 𝑥^2 – 𝑥 + 1 is neither strictly increasing nor strictly decreasing on (– 1, 1).Given f(𝑥) = 𝑥2 – 𝑥 + 1 Finding f’(𝒙) f’(𝑥) = 2𝑥 – 1 Putting f’(𝒙) = 0 2𝑥 – 1 = 0 2𝑥 = 1 𝑥 = 1/2 Since 𝒙 ∈ (−𝟏 , 𝟏) So, our number line looks like Hence, f(x) is strictly decreasing for 𝑥 ∈ (−1 , 1/2) & f(x) is strictly increasing for 𝑥 ∈ (1/2, 1) Hence, f(𝑥) is neither decreasing nor increasing on (−𝟏 , 𝟏). Hence Proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.