Examples 11 step 4.jpg

  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise


Example 11 Find the intervals in which the function f given by f (๐‘ฅ)=4๐‘ฅ3โˆ’6๐‘ฅ2โ€“72๐‘ฅ+30 is (a) strictly increasing (b) strictly decreasing. f (๐‘ฅ)=4๐‘ฅ3โˆ’6๐‘ฅ2 โ€“72๐‘ฅ+30 Step 1: Calculating fโ€™(x) f (๐‘ฅ)=4๐‘ฅ3โˆ’6๐‘ฅ2โ€“72๐‘ฅ+30 ๐‘“โ€ฒ(๐‘ฅ)=12๐‘ฅ2โˆ’12๐‘ฅ โ€“72๐‘ฅ ๐‘“โ€ฒ(๐‘ฅ) =12(๐‘ฅ2โˆ’๐‘ฅ โ€“6) ๐‘“โ€ฒ(๐‘ฅ) =12(๐‘ฅ2โˆ’3๐‘ฅ+2๐‘ฅ โ€“6) ๐‘“โ€ฒ(๐‘ฅ) =12(๐‘ฅ(๐‘ฅ โˆ’ 3) + 2(๐‘ฅ โˆ’ 3)) ๐‘“โ€ฒ(๐‘ฅ)=12(๐‘ฅ+2)(๐‘ฅ โ€“3) Step 2: Putting fโ€™(x) = 0 12(๐‘ฅ+2)(๐‘ฅ โ€“3)=0 (๐‘ฅ+2)(๐‘ฅ โ€“3)=0 So, x = โˆ’2 and x = 3 Step 3: Plotting point on real line The points divide the real line into 3 disjoint intervals. i.e. (โˆ’โˆž , โˆ’2) (โˆ’2 ,3 ) & (3 , โˆž) Step 4 (a) f is strictly increasing in (โˆ’โˆž ,โˆ’๐Ÿ) & (๐Ÿ‘ ,โˆž) (b) f is strictly decreasing in (โˆ’๐Ÿ, ๐Ÿ‘)

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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.