Misc 10 - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by

Misc 10 - Find points f(x) = (x-2)4 (x+1)3 has local maxima - Miscellaneous

part 2 - Misc 10 - Miscellaneous - Serial order wise - Chapter 6 Class 12 Application of Derivatives
part 3 - Misc 10 - Miscellaneous - Serial order wise - Chapter 6 Class 12 Application of Derivatives
part 4 - Misc 10 - Miscellaneous - Serial order wise - 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

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