Misc 10 - Chapter 6 Class 12 Application of Derivatives

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Misc 10 Find the points at which the function f given by f (𝑥) = (𝑥−2)^4 (𝑥+1)^3 has (i) local maxima (ii) local minima (iii) point of inflexionf(𝑥)= (𝑥−2)^4 (𝑥+1)3 Finding f’(𝒙) f’(𝑥) = (𝑑 ((𝑥 − 2)^4 (𝑥 + 1)^3 ))/𝑑𝑥 = 〖((𝑥−2)^4 )^′ (𝑥+1)〗^3+((𝑥+1)^3 )^′ (𝑥−2)^4 = 4(𝑥−2)^3 (𝑥+1)^3+3(𝑥+1)^2 (𝑥−2)^4 = (𝑥−2)^3 (𝑥+1)^2 [4(𝑥+1)+3(𝑥−2)] = (𝑥−2)^3 (𝑥+1)^2 [4𝑥+4+3𝑥−6] = (𝒙−𝟐)^𝟑 (𝒙+𝟏)^𝟐 [𝟕𝒙−𝟐] Putting f’(𝒙)=𝟎 (𝑥−2)^3 (𝑥+1)^2 (7𝑥−2)=0 Hence, 𝑥=2 & 𝑥=−1 & 𝑥=2/7 = 0.28 (𝑥−2)^3 = 0 𝑥 – 2 = 0 𝒙=𝟐 (𝑥+1)^2=0 (𝑥+1)=0 𝒙 = –1 7𝑥 – 2 = 0 7𝑥 = 2 𝒙 = 𝟐/𝟕 Thus, 𝑥=−𝟏 is a point of Inflexion 𝑥=𝟐/𝟕 is point of maxima 𝑥=𝟐 is point of minima

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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