Check sibling questions

Example 11 - Find intervals in which f(x) is strictly - Examples

Example 11 - Chapter 6 Class 12 Application of Derivatives - Part 2
Example 11 - Chapter 6 Class 12 Application of Derivatives - Part 3

This video is only available for Teachoo black users

Introducing your new favourite teacher - Teachoo Black, at only β‚Ή83 per month


Transcript

Example 11 Find the intervals in which the function f given by f (π‘₯)=4π‘₯3βˆ’6π‘₯2 –72π‘₯+30 is (a) strictly increasing (b) strictly decreasing. f (π‘₯)=4π‘₯3βˆ’6π‘₯2 –72π‘₯+30 Calculating f’(x) f (π‘₯)=4π‘₯3βˆ’6π‘₯2–72π‘₯+30 𝑓′(π‘₯)=12π‘₯2βˆ’12π‘₯ –72π‘₯ 𝑓′(π‘₯) =12(π‘₯2βˆ’π‘₯ – 6) 𝑓′(π‘₯) =12(π‘₯2βˆ’3π‘₯+2π‘₯ –6) 𝑓′(π‘₯) = 12(π‘₯(π‘₯ βˆ’ 3) + 2(π‘₯ βˆ’ 3)) 𝒇′(𝒙)=𝟏𝟐(𝒙+𝟐)(𝒙 β€“πŸ‘) Putting f’(x) = 0 12(π‘₯+2)(π‘₯ –3)=0 (π‘₯+2)(π‘₯ –3)=0 So, x = βˆ’2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (βˆ’βˆž ,βˆ’πŸ) & (πŸ‘ ,∞) f is strictly decreasing in (βˆ’πŸ, πŸ‘)

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.