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Last updated at April 16, 2024 by Teachoo

Example 18 (Method 1) Find all the points of local maxima and local minima of the function f given by f (đĽ)=2đĽ3 â6đĽ2+6đĽ+5.f (đĽ)=2đĽ3 â6đĽ2+ 6đĽ+5 Finding fâ (đ) f â˛(đĽ)= đ(2đĽ3 â 6đĽ2 + 6đĽ + 5)/đđĽ f â˛(đĽ)=6đĽ2 â12đĽ+6+0 f â˛(đĽ)=6(đĽ^2â2đĽ+1) Putting f â˛(đ)= 0 6(đĽ^2â2đĽ+1)=0 đĽ^2â2đĽ+1=0 (đĽ)^2+(1)^2â2(đĽ)(1)=0 (đĽâ1)^2=0 So, đ=đ is only critical point Hence đ=đ is point of inflexion Example 18 (Method 2) Find all the points of local maxima and local minima of the function f given by f (đĽ)=2đĽ3 â6đĽ2+6đĽ+5. f (đĽ)=2đĽ3 â6đĽ2+ 6đĽ+5 Finding fâ (đ) f â˛(đĽ)= đ(2đĽ3 â 6đĽ2+ 6đĽ + 5)/đđĽ f â˛(đĽ)=6đĽ2 â12đĽ+6+0 f â˛(đĽ)=6(đĽ^2â2đĽ+1) Putting f â˛(đ)= 0 6(đĽ^2â2đĽ+1)=0 đĽ^2â2đĽ+1=0 đĽ^2+1^2â2(đĽ)(1)=0 (đĽâ1)^2=0 So, đ=đ is only critical point Finding fââ(đ) fââ(đĽ)=6 đ(đĽ^2 â 2đĽ + 1)/đđĽ fââ(đĽ)=6(2đĽâ2+0) fââ(đĽ)=12(đĽâ1) Putting đ=đ fââ(1)=12(1â1) = 12 Ă 0 = 0 Since fââ(1) = 0 Hence, đĽ=1 is neither point of Maxima nor point of Minima â´ đ=đ is Point of Inflexion.