Examples

Chapter 6 Class 12 Application of Derivatives
Serial order wise

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Example 11 Find the intervals in which the function f given by f (π₯)=4π₯3β6π₯2 β72π₯+30 is (a) strictly increasing (b) strictly decreasing. f (π₯)=4π₯3β6π₯2 β72π₯+30 Calculating fβ(x) f (π₯)=4π₯3β6π₯2β72π₯+30 πβ²(π₯)=12π₯2β12π₯ β72π₯ πβ²(π₯) =12(π₯2βπ₯ β 6) πβ²(π₯) =12(π₯2β3π₯+2π₯ β6) πβ²(π₯) = 12(π₯(π₯ β 3) + 2(π₯ β 3)) πβ²(π)=ππ(π+π)(π βπ) Putting fβ(x) = 0 12(π₯+2)(π₯ β3)=0 (π₯+2)(π₯ β3)=0 So, x = β2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (ββ ,βπ) & (π ,β) f is strictly decreasing in (βπ, π)

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.