Last updated at April 19, 2021 by Teachoo

Transcript

Example 11 Find the intervals in which the function f given by f (๐ฅ)=4๐ฅ3โ6๐ฅ2 โ72๐ฅ+30 is (a) strictly increasing (b) strictly decreasing. f (๐ฅ)=4๐ฅ3โ6๐ฅ2 โ72๐ฅ+30 Calculating fโ(x) f (๐ฅ)=4๐ฅ3โ6๐ฅ2โ72๐ฅ+30 ๐โฒ(๐ฅ)=12๐ฅ2โ12๐ฅ โ72๐ฅ ๐โฒ(๐ฅ) =12(๐ฅ2โ๐ฅ โ 6) ๐โฒ(๐ฅ) =12(๐ฅ2โ3๐ฅ+2๐ฅ โ6) ๐โฒ(๐ฅ) = 12(๐ฅ(๐ฅ โ 3) + 2(๐ฅ โ 3)) ๐โฒ(๐)=๐๐(๐+๐)(๐ โ๐) Putting fโ(x) = 0 12(๐ฅ+2)(๐ฅ โ3)=0 (๐ฅ+2)(๐ฅ โ3)=0 So, x = โ2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (โโ ,โ๐) & (๐ ,โ) f is strictly decreasing in (โ๐, ๐)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.