Example 11 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 4, 2018 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)
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11 You are here
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23
Example 24
Example 25
Example 26
Example 27
Example 28
Example 29
Example 30
Example 31
Example 32
Example 33
Example 34
Example 35 Important
Example 36
Example 37 Important
Example 38 Important
Example 39
Example 40 Important
Example 41
Example 42
Example 43
Example 44
Example 45
Example 46 Important
Example 47 Important
Example 48
Example 49
Example 50
Example 51
Chapter 6 Class 12 Application of Derivatives
Serial order wise
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.