Ex 6.2,11 - Chapter 6 Class 12 Application of Derivatives

Last updated at August 13, 2026 by

Ex 6.2, 11 - Prove f(x) = x2-x+1 is neither strictly increasing

Ex 6.2,11 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.2,11 - Chapter 6 Class 12 Application of Derivatives - Part 3

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 2 questions, selected from your answers, mistakes, and progress.
Remove Ads
Teachoo ยท Class 12 Explore Class 12

Transcript

Ex 6.2, 11 Prove that the function f given by f (๐‘ฅ) = ๐‘ฅ^2 โ€“ ๐‘ฅ + 1 is neither strictly increasing nor strictly decreasing on (โ€“ 1, 1).Given f(๐‘ฅ) = ๐‘ฅ2 โ€“ ๐‘ฅ + 1 Finding fโ€™(๐’™) fโ€™(๐‘ฅ) = 2๐‘ฅ โ€“ 1 Putting fโ€™(๐’™) = 0 2๐‘ฅ โ€“ 1 = 0 2๐‘ฅ = 1 ๐‘ฅ = 1/2 Since ๐’™ โˆˆ (โˆ’๐Ÿ , ๐Ÿ) So, our number line looks like Hence, f(x) is strictly decreasing for ๐‘ฅ โˆˆ (โˆ’1 , 1/2) & f(x) is strictly increasing for ๐‘ฅ โˆˆ (1/2, 1) Hence, f(๐‘ฅ) is neither decreasing nor increasing on (โˆ’๐Ÿ , ๐Ÿ). Hence Proved

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.