Ex 6.2,18 - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by

Ex 6.2, 18 - Prove that f(x) = x3 - 3x2 + 3x - 100 is increasing

Ex 6.2,18 - Chapter 6 Class 12 Application of Derivatives - Part 2

Go Ad-free

Transcript

Ex 6.2, 18 Prove that the function given by f (𝑥) = 𝑥3 – 3𝑥2 + 3𝑥 – 100 is increasing in R. We need to show f(𝑥) is strictly increasing on R i.e. we need to show f’(𝒙) > 0 Finding f’(𝒙) f’(𝑥)= 3x2 – 6x + 3 – 0 = 3(𝑥2−2𝑥+1) = 3((𝑥)2+(1)2−2(𝑥)(1)) = 3(𝑥−1)2 Since Square of any number is always positive (𝑥−1)2 > 0 3(𝑥−1)2>0 f’(𝒙) > 0 Hence, f’(𝑥) > 0 for all values of 𝑥 ∴ f(𝑥) is strictly increasing on R

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 and Computer Science at Teachoo