Check sibling questions

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

(A) R Β 

(B) R βˆ’ {3}

(C) (0, ∞) 

(D) None of these

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

Slide37.JPG

Slide38.JPG
Slide39.JPG


Transcript

Question 8 The set of points where the functions f given by f (x) = |x – 3| cos x is differentiable is (A) R (B) R βˆ’ {3} (C) (0, ∞) (D) None of these f(x) = |π‘₯βˆ’3| cos⁑π‘₯ = {β–ˆ((π‘₯βˆ’3) cos⁑π‘₯, π‘₯βˆ’3β‰₯0@βˆ’(π‘₯βˆ’3) cos⁑π‘₯, π‘₯βˆ’3<0)─ = {β–ˆ((π‘₯βˆ’3) cos⁑π‘₯, π‘₯β‰₯3@βˆ’(π‘₯βˆ’3) cos⁑π‘₯, π‘₯<3)─ Now, f(x) is a differentiable at x = 3 if LHD = RHD (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) (𝒇(𝒙) βˆ’ 𝒇(𝒙 βˆ’ 𝒉))/𝒉 = (π‘™π‘–π‘š)┬(hβ†’0) (𝑓(3) βˆ’ 𝑓(3 βˆ’ β„Ž))/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (|3 βˆ’ 3| cos⁑3βˆ’|(3 βˆ’ β„Ž)βˆ’3| cos⁑〖(3 βˆ’ β„Ž)γ€—)/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (0 βˆ’|3 βˆ’ β„Ž βˆ’3| cos⁑〖(3 βˆ’ β„Ž)γ€—)/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (0 βˆ’|βˆ’β„Ž| cos⁑〖(3 βˆ’ β„Ž)γ€—)/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (βˆ’β„Ž cos⁑〖(3 βˆ’ β„Ž)γ€—)/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) βˆ’cos⁑〖(3 βˆ’β„Ž)γ€— = βˆ’cos⁑〖(3 βˆ’0)γ€— = βˆ’π’„π’π’”β‘πŸ‘ (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) (𝒇(𝒙+𝒉) βˆ’ 𝒇(𝒙 ))/𝒉 = (π‘™π‘–π‘š)┬(hβ†’0) (𝑓(3+β„Ž) βˆ’ 𝑓(3))/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (|(3+β„Ž) βˆ’ 3| cos⁑〖(3+β„Ž)γ€—βˆ’|3 βˆ’ 3| cos⁑〖(3)γ€—)/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (|3 + β„Ž βˆ’3| cos⁑(3 + β„Ž)βˆ’0 )/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (| β„Ž| cos⁑〖(3+β„Ž)γ€—)/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) (β„Ž cos⁑〖(3 + β„Ž)γ€—)/β„Ž = (π‘™π‘–π‘š)┬(hβ†’0) cos⁑〖(3+β„Ž)γ€— = cos⁑〖(3+0)γ€— = π’„π’π’”β‘πŸ‘ Since LHD β‰  RHD ∴ f(x) is not differentiable at x = 3 Hence, we can say that f(x) is differentiable on R βˆ’ {πŸ‘} So, the correct answer is (B)

Davneet Singh's photo - Teacher, Engineer, Marketer

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.