Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Last updated at May 29, 2018 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Continuity and Differentiability Class 12

Transcript

Misc 18 If 𝑓 (𝑥)=|𝑥 3, show that 𝑓 ″(𝑥) exists for all real 𝑥 and find it. We know that 𝑥= 𝑥 𝑥≥0−𝑥 𝑥<0 𝑓 (𝑥)=|𝑥 3 = 𝑥3 , 𝑥≥0 −𝑥3 , 𝑥<0 = 𝑥3 , 𝑥≥0 −𝑥3 , 𝑥<0 Case 1 :- When 𝑥≥0 𝑓 (𝑥)= 𝑥3 Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑓′(𝑥)= 3𝑥2 Again Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑓′′(𝑥)= 3 𝑥2′ 𝑓′′(𝑥)= 6𝑥 Hence 𝑓′′(𝑥)=6𝑥 exist for all value of 𝑥 greater than 0. Case 2 :- When 𝑥<0 𝑓 (𝑥)= −𝑥3 Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑓′ 𝑥= −𝑥3′ 𝑓′(𝑥)= −3𝑥2 Again Differentiating 𝑤.𝑟.𝑡.𝑥. 𝑓′′(𝑥)= −3𝑥2′ 𝑓′′ 𝑥= −6𝑥 Hence 𝑓′′ 𝑥=−6𝑥 exist for all value of 𝑥 less than 0 .

Miscellaneous

Misc 1

Misc 2

Misc 3

Misc 4

Misc 5 Important

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18 You are here

Misc 19 Important

Misc 20

Misc 21

Misc 22

Misc 23 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.