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Last updated at May 6, 2021 by Teachoo

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Example 30 (Method 1) 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 So, ๐=๐ 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 So, ๐=๐ is only critical point Finding fโโ(๐) fโโ(๐ฅ)=6 ๐(๐ฅ^2 โ 2๐ฅ + 1)/๐๐ฅ fโโ(๐ฅ)=6(2๐ฅโ2+0) fโโ(๐ฅ)=12(๐ฅโ1) Putting ๐=๐ fโโ(1)=12(1โ1) = 12 ร 0 = 0 Since fโโ(1) = 0 Hence, ๐ฅ=1 is neither point of Maxima nor point of Minima โด ๐=๐ is Point of Inflexion.

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Chapter 6 Class 12 Application of Derivatives (Term 1)

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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.