# Ex 6.2,15

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 6.2,15 Let I be any interval disjoint from [–1, 1]. Prove that the function f given by 𝑓(𝑥) = 𝑥 + 1𝑥 is strictly increasing on I. I is any interval disjoint from [–1, 1] Hence I = − −1 𝑢1, uc1 f𝑥 = 𝑥 + 1𝑥 We need to show f𝑥 is strictly increasing on I i.e. we need to show f’𝑥 > 0 for 𝑥 ∈− −1 𝑢1, uc1 Step 1: Finding f’𝑥 f𝑥 = 𝑥 + 1𝑥 f’𝑥 = 1 – 1𝑥2 f’𝑥 = 𝑥2 − 1𝑥2 f’𝑥 = 1𝑥2𝑥−1𝑥+1 Step 2: Putting f’𝑥 = 0 𝑥2 − 1𝑥2 = 0 𝑥2−1 = 0 𝑥−1𝑥+1=0 So, 𝑥=1 & 𝑥=−1 Step 3: Plotting point on real line The point 𝑥 = –1 , 1 into three disjoint intervals i.e. − −1 −1 , 1 & 1 , uc1 Step 4: ∴ f𝑥 is strictly increasing on − −𝟏 & 𝟏 , uc1 Hence proved

Chapter 6 Class 12 Application of Derivatives

Serial order wise

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CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .