Example 21 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 21 (Method 2) Find all the points of local maxima and local minima of the function f given by đ(đĽ)=2đĽ3 â6đĽ2+6đĽ+5. đ(đĽ)=2đĽ3 â6đĽ2+6đĽ+5 Finding fâ(đ) đâ(đĽ)=đ(2đĽ3 â 6đĽ2 + 6đĽ + 5" " )/đđĽ đâ(đĽ)=6đĽ^2â12đĽ+6++0 đâ(đĽ)=6(đĽ^2â2đĽ+1) đâ(đĽ)=6((đĽ)^2+(1)^2â2(đĽ)(1)) đâ(đĽ)=đ(đâđ)^đ Putting fâ(đ)=đ 6(đĽâ1)^2=0 (đĽâ1)^2=0 So, đ=đ is the only critical point Finding fââ(đ) fââ(đĽ)=6.(đ(đĽ â 1)^2)/đđĽ fââ(đĽ)=6 Ă 2(đĽâ1) fââ(đĽ) = 12 (đĽâ1) Putting đ=đ fââ(đĽ)=12(1â1) = 0 Since fââ(1) = 0 Hence, đĽ=1 is neither point of Maxima nor point of Minima â´ đ=đ is Point of Inflexion.
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo