Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12




Last updated at Jan. 7, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12
Transcript
Example 30 (Method 1) Find all the points of local maxima and local minima of the unction f given by f (๐ฅ)=2๐ฅ3 โ6๐ฅ2+6๐ฅ+5. f (๐ฅ)=2๐ฅ3 โ6๐ฅ2+ 6๐ฅ+5 Finding fโ (๐) f โฒ(๐ฅ)= ๐(2๐ฅ3 โ 6๐ฅ2 + 6๐ฅ + 5)/๐๐ฅ f โฒ(๐ฅ)=6๐ฅ2 โ12๐ฅ+6+0 f โฒ(๐ฅ)=6(๐ฅ^2โ2๐ฅ+1) Putting f โฒ(๐)= 0 6(๐ฅ^2โ2๐ฅ+1)=0 ๐ฅ^2โ2๐ฅ+1=0 (๐ฅ)^2+(1)^2โ2(๐ฅ)(1)=0 (๐ฅโ1)^2=0 (๐ฅโ1)(๐ฅโ1)=0 So, ๐ฅ=1 is only critical point Hence ๐=๐ is point of inflexion Example 30 (Method 2) Find all the points of local maxima and local minima of the function f given by f (๐ฅ)=2๐ฅ3 โ6๐ฅ2+6๐ฅ+5. f (๐ฅ)=2๐ฅ3 โ6๐ฅ2+ 6๐ฅ+5 Finding fโ (๐) f โฒ(๐ฅ)= ๐(2๐ฅ3 โ 6๐ฅ2+ 6๐ฅ + 5)/๐๐ฅ f โฒ(๐ฅ)=6๐ฅ2 โ12๐ฅ+6+0 f โฒ(๐ฅ)=6(๐ฅ^2โ2๐ฅ+1) Putting f โฒ(๐)= 0 6(๐ฅ^2โ2๐ฅ+1)=0 ๐ฅ^2โ2๐ฅ+1=0 ๐ฅ^2+1^2โ2(๐ฅ)(1)=0 (๐ฅโ1)^2=0 (๐ฅโ1)(๐ฅโ1)=0 So, ๐ฅ=1 is only critical point Finding fโโ(๐) fโ(๐ฅ)=6(๐ฅ^2โ2๐ฅ+1) fโโ(๐ฅ)=6๐(๐ฅ^2 โ 2๐ฅ + 1)/๐๐ฅ fโโ(๐ฅ)=6(2๐ฅโ2+0) fโโ(๐ฅ)=12(๐ฅโ1) Putting ๐ฅ=1 fโโ(1)=12(1โ1) = 12 ร 0 = 0 Thus, second derivative test fails Hence, ๐ฅ=1 is neither point of Maxima nor point of Minima โด ๐=๐ is Point of Inflexion.
Examples
Example 2 Not in Syllabus - CBSE Exams 2021
Example 3 Not in Syllabus - CBSE Exams 2021
Example 4 Important Not in Syllabus - CBSE Exams 2021
Example 5 Not in Syllabus - CBSE Exams 2021
Example 6 Not in Syllabus - CBSE Exams 2021
Example 7
Example 8 Important
Example 9 Important
Example 10
Example 11 Important
Example 12
Example 13 Important
Example 14
Example 15
Example 16
Example 17 Important
Example 18
Example 19
Example 20
Example 21 Not in Syllabus - CBSE Exams 2021
Example 22 Not in Syllabus - CBSE Exams 2021
Example 23 Not in Syllabus - CBSE Exams 2021
Example 24
Example 25
Example 26
Example 27
Example 28 Important
Example 29
Example 30 Important You are here
Example 31
Example 32 Important
Example 33 Important
Example 34
Example 35 Important
Example 36
Example 37 Important
Example 38 Important
Example 39
Example 40 Important
Example 41 Important
Example 42 Important Not in Syllabus - CBSE Exams 2021
Example 43 Important Not in Syllabus - CBSE Exams 2021
Example 44 Important Not in Syllabus - CBSE Exams 2021
Example 45 Important
Example 46 Important
Example 47 Important
Example 48 Important
Example 49 Not in Syllabus - CBSE Exams 2021
Example 50 Important
Example 51
About the Author