Example 11 - Chapter 6 Class 12 Application of Derivatives
Last updated at Feb. 22, 2019 by Teachoo
Transcript
Example 11 Find the intervals in which the function f given by f (๐ฅ)=4๐ฅ3โ6๐ฅ2โ72๐ฅ+30 is (a) strictly increasing (b) strictly decreasing. f (๐ฅ)=4๐ฅ3โ6๐ฅ2 โ72๐ฅ+30 Step 1: Calculating fโ(x) f (๐ฅ)=4๐ฅ3โ6๐ฅ2โ72๐ฅ+30 ๐โฒ(๐ฅ)=12๐ฅ2โ12๐ฅ โ72๐ฅ ๐โฒ(๐ฅ) =12(๐ฅ2โ๐ฅ โ6) ๐โฒ(๐ฅ) =12(๐ฅ2โ3๐ฅ+2๐ฅ โ6) ๐โฒ(๐ฅ) =12(๐ฅ(๐ฅ โ 3) + 2(๐ฅ โ 3)) ๐โฒ(๐ฅ)=12(๐ฅ+2)(๐ฅ โ3) Step 2: Putting fโ(x) = 0 12(๐ฅ+2)(๐ฅ โ3)=0 (๐ฅ+2)(๐ฅ โ3)=0 So, x = โ2 and x = 3 Step 3: Plotting point on real line The points divide the real line into 3 disjoint intervals. i.e. (โโ , โ2) (โ2 ,3 ) & (3 , โ) Step 4 (a) f is strictly increasing in (โโ ,โ๐) & (๐ ,โ) (b) f is strictly decreasing in (โ๐, ๐)
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Chapter 6 Class 12 Application of Derivatives
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.