Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at Jan. 3, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12
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 (โ5) 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^โฒ (๐)=(๐(๐) โ ๐(๐))/(๐ โ ๐) Given that ๐^โฒ (๐ฅ) does not vanish any where โ ๐^โฒ (๐ฅ) โ 0 for any value of x Thus, ๐^โฒ (๐) โ 0 (๐(5) โ ๐(โ5))/(5 โ(โ5) ) โ 0 (๐(5) โ ๐(โ5))/(5 + 5) โ 0 ๐(5)โ ๐(โ5) โ 0 ร 10 ๐(5)โ ๐(โ5) โ 0 ๐(5) "โ " ๐(โ5) Hence proved.
Ex 5.8
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