NCERT Exemplar - MCQs

Chapter 5 Class 12 Continuity and Differentiability
Serial order wise

## (D) None of these

This question is similar to Ex 5.2, 9 - Chapter 5 Class 12 - Continuity and Differentiability

### Transcript

Question 8 The set of points where the functions f given by f (x) = |x โ 3| cos x is differentiable is (A) R (B) R โ {3} (C) (0, โ) (D) None of these f(x) = |๐ฅโ3| cosโก๐ฅ = {โ((๐ฅโ3) cosโก๐ฅ, ๐ฅโ3โฅ0@โ(๐ฅโ3) cosโก๐ฅ, ๐ฅโ3<0)โค = {โ((๐ฅโ3) cosโก๐ฅ, ๐ฅโฅ3@โ(๐ฅโ3) cosโก๐ฅ, ๐ฅ<3)โค Now, f(x) is a differentiable at x = 3 if LHD = RHD (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(๐ โ ๐))/๐ = (๐๐๐)โฌ(hโ0) (๐(3) โ ๐(3 โ โ))/โ = (๐๐๐)โฌ(hโ0) (|3 โ 3| cosโก3โ|(3 โ โ)โ3| cosโกใ(3 โ โ)ใ)/โ = (๐๐๐)โฌ(hโ0) (0 โ|3 โ โ โ3| cosโกใ(3 โ โ)ใ)/โ = (๐๐๐)โฌ(hโ0) (0 โ|โโ| cosโกใ(3 โ โ)ใ)/โ = (๐๐๐)โฌ(hโ0) (โโ cosโกใ(3 โ โ)ใ)/โ = (๐๐๐)โฌ(hโ0) โcosโกใ(3 โโ)ใ = โcosโกใ(3 โ0)ใ = โ๐๐๐โก๐ (๐๐๐)โฌ(๐กโ๐) (๐(๐+๐) โ ๐(๐ ))/๐ = (๐๐๐)โฌ(hโ0) (๐(3+โ) โ ๐(3))/โ = (๐๐๐)โฌ(hโ0) (|(3+โ) โ 3| cosโกใ(3+โ)ใโ|3 โ 3| cosโกใ(3)ใ)/โ = (๐๐๐)โฌ(hโ0) (|3 + โ โ3| cosโก(3 + โ)โ0 )/โ = (๐๐๐)โฌ(hโ0) (| โ| cosโกใ(3+โ)ใ)/โ = (๐๐๐)โฌ(hโ0) (โ cosโกใ(3 + โ)ใ)/โ = (๐๐๐)โฌ(hโ0) cosโกใ(3+โ)ใ = cosโกใ(3+0)ใ = ๐๐๐โก๐ Since LHD โ  RHD โด f(x) is not differentiable at x = 3 Hence, we can say that f(x) is differentiable on R โ {๐} So, the correct answer is (B)