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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 13 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.