Ex 6.2, 6 (c) - Chapter 6 Class 12 Application of Derivatives

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Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 5

Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 6
Ex 6.2,6 - Chapter 6 Class 12 Application of Derivatives - Part 7

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Ex 6.2, 6 Find the intervals in which the following functions are strictly increasing or decreasing: (c) –2𝑥3 – 9𝑥2 – 12𝑥 + 1 f(𝑥) = –2𝑥3 – 9𝑥2 – 12𝑥 + 1 Calculating f’(𝒙) f’(𝑥) = –6𝑥2 –18𝑥 – 12 + 0 f’(𝑥) = –6(𝑥2+3𝑥+2) f’(𝑥) = –6(𝑥2+2𝑥+𝑥+2) f’(𝑥) = –6(𝑥(𝑥+2)+1(𝑥+2)) f’(𝒙) = –6(𝒙+𝟏) (𝒙+𝟐) Putting f’(𝒙) = 0 – 6(𝑥+1) (𝑥+2) = 0 (𝑥+1) (𝑥+2) = 0 So, 𝑥 = –1 , –2 Plotting points on number line Hence, f is strictly increasing for –2 < 𝒙 < –1 & strictly decreasing for 𝒙 < –2 & 𝒙 > –1 Hence, f is strictly increasing for –2 < 𝒙 < –1 & strictly decreasing for 𝒙 < –2 & 𝒙 > –1

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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