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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


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‘)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.