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Last updated at April 16, 2024 by Teachoo

Misc 10 Find the points at which the function f given by f (đĽ) = (đĽâ2)^4 (đĽ+1)^3 has (i) local maxima (ii) local minima (iii) point of inflexionf(đĽ)= (đĽâ2)^4 (đĽ+1)3 Finding fâ(đ) fâ(đĽ) = (đ ((đĽ â 2)^4 (đĽ + 1)^3 ))/đđĽ = ă((đĽâ2)^4 )^â˛ (đĽ+1)ă^3+((đĽ+1)^3 )^â˛ (đĽâ2)^4 = 4(đĽâ2)^3 (đĽ+1)^3+3(đĽ+1)^2 (đĽâ2)^4 = (đĽâ2)^3 (đĽ+1)^2 [4(đĽ+1)+3(đĽâ2)] = (đĽâ2)^3 (đĽ+1)^2 [4đĽ+4+3đĽâ6] = (đâđ)^đ (đ+đ)^đ [đđâđ] Putting fâ(đ)=đ (đĽâ2)^3 (đĽ+1)^2 (7đĽâ2)=0 Hence, đĽ=2 & đĽ=â1 & đĽ=2/7 = 0.28 (đĽâ2)^3 = 0 đĽ â 2 = 0 đ=đ (đĽ+1)^2=0 (đĽ+1)=0 đ = â1 7đĽ â 2 = 0 7đĽ = 2 đ = đ/đ Thus, đĽ=âđ is a point of Inflexion đĽ=đ/đ is point of maxima đĽ=đ is point of minima