NCERT Exemplar - MCQs

Chapter 5 Class 12 Continuity and Differentiability
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## (D) None of these

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

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### Transcript

Question 8 The set of points where the functions f given by f (x) = |x β 3| cos x is differentiable is (A) R (B) R β {3} (C) (0, β) (D) None of these f(x) = |π₯β3| cosβ‘π₯ = {β((π₯β3) cosβ‘π₯, π₯β3β₯[email protected]β(π₯β3) cosβ‘π₯, π₯β3<0)β€ = {β((π₯β3) cosβ‘π₯, π₯β₯[email protected]β(π₯β3) cosβ‘π₯, π₯<3)β€ Now, f(x) is a differentiable at x = 3 if LHD = RHD (πππ)β¬(π‘βπ) (π(π) β π(π β π))/π = (πππ)β¬(hβ0) (π(3) β π(3 β β))/β = (πππ)β¬(hβ0) (|3 β 3| cosβ‘3β|(3 β β)β3| cosβ‘γ(3 β β)γ)/β = (πππ)β¬(hβ0) (0 β|3 β β β3| cosβ‘γ(3 β β)γ)/β = (πππ)β¬(hβ0) (0 β|ββ| cosβ‘γ(3 β β)γ)/β = (πππ)β¬(hβ0) (ββ cosβ‘γ(3 β β)γ)/β = (πππ)β¬(hβ0) βcosβ‘γ(3 ββ)γ = βcosβ‘γ(3 β0)γ = βπππβ‘π (πππ)β¬(π‘βπ) (π(π+π) β π(π ))/π = (πππ)β¬(hβ0) (π(3+β) β π(3))/β = (πππ)β¬(hβ0) (|(3+β) β 3| cosβ‘γ(3+β)γβ|3 β 3| cosβ‘γ(3)γ)/β = (πππ)β¬(hβ0) (|3 + β β3| cosβ‘(3 + β)β0 )/β = (πππ)β¬(hβ0) (| β| cosβ‘γ(3+β)γ)/β = (πππ)β¬(hβ0) (β cosβ‘γ(3 + β)γ)/β = (πππ)β¬(hβ0) cosβ‘γ(3+β)γ = cosβ‘γ(3+0)γ = πππβ‘π Since LHD β  RHD β΄ f(x) is not differentiable at x = 3 Hence, we can say that f(x) is differentiable on R β {π} So, the correct answer is (B)