web analytics

Example 11 - Find intervals in which f(x) is strictly - Find intervals of increasing/decreasing

Slide33.JPG
Slide34.JPG

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

Transcript

Example 11 Find the intervals in which the function f given by f ﷐𝑥﷯=4𝑥3−6𝑥2–72𝑥+30 is (a) strictly increasing (b) strictly decreasing. f ﷐𝑥﷯=4𝑥3−6𝑥2 –72𝑥+30 Step 1: Calculating f’(x) f ﷐𝑥﷯=4𝑥3−6𝑥2–72𝑥+30 𝑓′﷐𝑥﷯=12𝑥2−12𝑥 –72𝑥 𝑓′﷐𝑥﷯ =12﷐𝑥2−𝑥 –6﷯ 𝑓′﷐𝑥﷯ =12﷐𝑥2−2𝑥 −3𝑥 –6﷯ 𝑓′(𝑥) =12(𝑥(𝑥 − 2) − 3(𝑥 − 2)) 𝑓′﷐𝑥﷯=12﷐𝑥−2﷯﷐𝑥 –3﷯ Step 2: Putting f’(x) = 0 12﷐𝑥−2﷯﷐𝑥−3﷯=0 ﷐𝑥−2﷯﷐𝑥−3﷯=0 So, x = 2 and x = 3 Step 3: Plotting point on real line The points divide the real line into 3 disjoint intervals. i.e. ﷐−𕔴 2﷯ ﷐2 ,3 ﷯ & ﷐3 , 𕔴uc1﷯ Step 4: (a) f is strictly increasing in ﷐−𕔴 ,𝟐﷯ & ﷐𝟑 ,𕔴uc1﷯ (b) f is strictly decreasing in ﷐𝟐, 𝟑﷯

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 provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail