Slide72.JPG

Slide73.JPG
Slide74.JPG

Go Ad-free

Transcript

Ex 6.3, 28 For all real values of x, the minimum value of (1 − 𝑥 + 𝑥2)/(1 + 𝑥 + 𝑥2) is (A) 0 (B) 1 (C) 3 (D) 1/3Let 𝑓(𝑥)=(1 − 𝑥 + 𝑥2)/(1 + 𝑥 + 𝑥2) Finding 𝒇′(𝒙) 𝑓(𝑥)=(1 − 𝑥 + 𝑥2)/(1 + 𝑥 + 𝑥2) 𝑓^′(𝑥) =((1 − 𝑥 + 𝑥^2 )^′ (1 + 𝑥 + 𝑥^2 ) − (1 − 𝑥 + 𝑥^2 ) (1 + 𝑥 + 𝑥^2 )^′)/(1 + 𝑥 + 𝑥^2 )^2 𝑓′(𝑥)=(−1 − 𝑥 − 𝑥^2 + 2𝑥 + 2𝑥^2+ 2𝑥^3 − (1 − 𝑥 + 𝑥^2+ 2𝑥 − 2𝑥^2 + 2𝑥^3 ))/(1 + 𝑥 + 𝑥^2 )^2 𝑓(𝑥)=(−1 + 𝑥 + 𝑥^2 + 2𝑥^3 − (1 + 𝑥 − 𝑥^2 + 2𝑥^3 ))/(1 + 𝑥 + 𝑥^2 )^2 𝑓′(𝑥)=(−2 + 2𝑥^2)/(1 + 𝑥 + 𝑥^2 )^2 Putting 𝒇^′ (𝒙)=𝟎 (−2 + 2𝑥^2)/(1 + 𝑥 + 𝑥^2 )^2 =0 2𝑥^2−2=0 2𝑥^2=2 𝑥^2=1 𝑥=±1 Hence, x = 1 or x = –1 are the critical points Finding value of 𝒇(𝒙) at critical points Hence, minimum value of f(x) is 1/3. So, (D) is the correct answer

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