# Ex 5.8, 3 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 5.8, 3 If ๐ : [โ 5, 5] โ ๐ is a differentiable function and if ๐ โฒ(๐ฅ) does not vanish anywhere, then prove that ๐ (โ 5) โ ๐ (5). ๐ : [โ 5, 5] โ ๐ is a differentiable โ We know that every differentiable function is continuous. Therefore f is continuous & differentiable both on (โ5, 5) By Mean Value Theorem There exist some c in (5, โ5) Such that ๐๏ทฎโฒ๏ทฏ ๐๏ทฏ= ๐ ๐๏ทฏ โ ๐ ๐๏ทฏ๏ทฎ๐ โ ๐๏ทฏ Given that ๐๏ทฎโฒ๏ทฏ ๐ฅ๏ทฏ does not vanish any where โ ๐๏ทฎโฒ๏ทฏ ๐ฅ๏ทฏ โ 0 for any value of x Thus, ๐๏ทฎโฒ๏ทฏ ๐๏ทฏ โ 0 ๐ 5๏ทฏ โ ๐ โ5๏ทฏ๏ทฎ5 โ โ5๏ทฏ๏ทฏ โ 0 ๐ 5๏ทฏ โ ๐ โ5๏ทฏ๏ทฎ5 + 5๏ทฏ โ 0 ๐ 5๏ทฏ โ ๐ โ5๏ทฏ โ 0 ร 10 ๐ 5๏ทฏ โ ๐ โ5๏ทฏ โ 0 ๐ 5๏ทฏ โ ๐ โ5๏ทฏ Hence proved.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.