Misc 7 - Find intervals f(x) = x3 + 1/x3 x = 0 is increasing - Miscellaneous

Slide36.JPG
Slide37.JPG Slide38.JPG

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
Ask Download

Transcript

Misc 7 Find the intervals in which the function f given by f (x) = x3 + 1﷮ 𝑥﷮3﷯﷯ , 𝑥 ≠ 0 is (i) increasing (ii) decreasing. f 𝑥﷯ = 𝑥3 + 1﷮𝑥3﷯ Step 1: Finding f’ 𝑥﷯ f’ 𝑥﷯ = 𝑑﷮𝑑𝑥﷯ 𝑥﷮3﷯+ 𝑥﷮−3﷯﷯﷮.﷯ = 3𝑥2 + −3﷯﷮−3 − 1﷯ = 3𝑥2 – 3 𝑥﷮−4﷯ = 3 𝑥﷮2﷯− 3﷮ 𝑥﷮4﷯﷯ = 3 𝑥﷮2﷯− 1﷮ 𝑥﷮4﷯﷯﷯ Step 2: Putting f’ 𝑥﷯ = 0 3 𝑥﷮2﷯− 1﷮ 𝑥﷮4﷯﷯﷯ = 0 𝑥﷮2﷯− 1﷮ 𝑥﷮4﷯﷯ = 0 𝑥﷮6﷯ − 1﷮ 𝑥﷮4﷯﷯ = 0 𝑥﷮6﷯−1 = 0 𝑥﷮3﷯﷯﷮2﷯− 1﷯﷮2﷯=0 𝑥﷮3﷯−1﷯ 𝑥﷮3﷯+1﷯=0 Hence, 𝑥 = 1 & –1 Step 3: Plotting value of 𝑥 on real line Thus, 𝑥 = –1 & 1 divide the real line into three disjoint intervals i.e. −唴−1﷯ −1, 1﷯& 1,唴﷯ Hence, f 𝑥﷯ is strictly increasing on −唴 −𝟏﷯ & 𝟏 , 唴﷯ & strictly decreasing on −𝟏 , 𝟏﷯

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.