Question 8 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability (Term 1)

Last updated at Nov. 17, 2021 by Teachoo

Hello! We hope that the questions explained by Teachoo are helping you for your Board exams. If Teachoo has been of any help to you, would you consider making a donation to support us? Please click on this link to support us.

The set of points where the functions
f
given by
f
(x) = |x β 3| cos x is differentiable is

Hello! We hope that the questions explained by Teachoo are helping you for your Board exams. If Teachoo has been of any help to you, would you consider making a donation to support us? Please click on this link to support us.

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₯β3| cosβ‘π₯
= {β((π₯β3) cosβ‘π₯, π₯β3β₯0@β(π₯β3) cosβ‘π₯, π₯β3<0)β€
= {β((π₯β3) cosβ‘π₯, π₯β₯3@β(π₯β3) cosβ‘π₯, π₯<3)β€
Now,
f(x) is a differentiable at x = 3 if
LHD = RHD
(πππ)β¬(π‘βπ) (π(π) β π(π β π))/π
= (πππ)β¬(hβ0) (π(3) β π(3 β β))/β
= (πππ)β¬(hβ0) (|3 β 3| cosβ‘3β|(3 β β)β3| cosβ‘γ(3 β β)γ)/β
= (πππ)β¬(hβ0) (0 β|3 β β β3| cosβ‘γ(3 β β)γ)/β
= (πππ)β¬(hβ0) (0 β|ββ| cosβ‘γ(3 β β)γ)/β
= (πππ)β¬(hβ0) (ββ cosβ‘γ(3 β β)γ)/β
= (πππ)β¬(hβ0) βcosβ‘γ(3 ββ)γ
= βcosβ‘γ(3 β0)γ
= βπππβ‘π
(πππ)β¬(π‘βπ) (π(π+π) β π(π ))/π
= (πππ)β¬(hβ0) (π(3+β) β π(3))/β
= (πππ)β¬(hβ0) (|(3+β) β 3| cosβ‘γ(3+β)γβ|3 β 3| cosβ‘γ(3)γ)/β
= (πππ)β¬(hβ0) (|3 + β β3| cosβ‘(3 + β)β0 )/β
= (πππ)β¬(hβ0) (| β| cosβ‘γ(3+β)γ)/β
= (πππ)β¬(hβ0) (β cosβ‘γ(3 + β)γ)/β
= (πππ)β¬(hβ0) cosβ‘γ(3+β)γ
= cosβ‘γ(3+0)γ
= πππβ‘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)

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.