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Last updated at April 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.