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

Last updated at April 16, 2024 by

 

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

Transcript

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

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.