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Misc 10 - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2023 by

Misc 13 - Find points f(x) = (x-2)4 (x+1)3 has local maxima

Misc 13 - Chapter 6 Class 12 Application of Derivatives - Part 2
Misc 13 - Chapter 6 Class 12 Application of Derivatives - Part 3 Misc 13 - Chapter 6 Class 12 Application of Derivatives - Part 4

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Misc 10 Find the points at which the functionf(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 Using product rule as (𝑢𝑣)^′=𝑢^′ 𝑣+𝑣^′ 𝑢 = 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 f given by f (𝑥) = (𝑥−2)^4 (𝑥+1)^3 has (i) local maxima (ii) local minima (iii) point of inflexion7𝑥 – 2 = 0 7𝑥 = 2 𝒙 = 𝟐/𝟕

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.