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 5.2, 9 Prove that the function f given by ๐ (๐ฅ) = | ๐ฅ โ 1|, ๐ฅ โ ๐ is not differentiable at x = 1. f(x) = |๐ฅโ1| = {โ((๐ฅโ1), ๐ฅโ1โฅ0@โ(๐ฅโ1), ๐ฅโ1<0)โค = {โ((๐ฅโ1), ๐ฅโฅ1@โ(๐ฅโ1), ๐ฅ<1)โค Now, f(x) is a differentiable at x = 1 if LHD = RHD (๐๐๐)โฌ(hโ0) (๐(๐ฅ) โ ๐(๐ฅ โ โ))/โ = (๐๐๐)โฌ(hโ0) (๐(1) โ ๐(1 โ โ))/โ = (๐๐๐)โฌ(hโ0) ((1 โ 1) โ(โ((1 โ โ) โ 1)))/โ = (๐๐๐)โฌ(hโ0) (0 + (1 โ โ โ 1))/โ = (๐๐๐)โฌ(hโ0) (0 โ โ)/โ = (๐๐๐)โฌ(hโ0) (โโ)/โ = (๐๐๐)โฌ(hโ0) (โ1) = โ1 (๐๐๐)โฌ(hโ0) (๐(๐ฅ + โ) โ ๐(๐ฅ))/โ = (๐๐๐)โฌ(hโ0) (๐(1 + โ) โ ๐(1))/โ = (๐๐๐)โฌ(hโ0) (((1 + โ) โ 1) โ (1 โ 1))/โ = (๐๐๐)โฌ(hโ0) (โ โ 0)/โ = (๐๐๐)โฌ(hโ0) โ/โ = (๐๐๐)โฌ(hโ0) (1) = 1 Since LHD โ RHD โด f(x) is not differentiable at x = 1 Hence proved
Checking if funciton is differentiable
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