Ex 6.2, 8 - Find x for which y = x(x - 2)2 is increasing

Ex 6.2,8 - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.2,8 - Chapter 6 Class 12 Application of Derivatives - Part 3
Ex 6.2,8 - Chapter 6 Class 12 Application of Derivatives - Part 4

Go Ad-free

Transcript

Ex 6.2, 8 Find the values of 𝑥 for which y = [𝑥(𝑥 – 2)]2 is an increasing function 𝑦 = [𝑥(𝑥−2)]^2 Finding 𝒅𝒚/𝒅𝒙 𝑦 = [𝑥(𝑥−2)]^2 𝑦 = [𝑥^2−2𝑥]^2 𝑦 = (𝑥)^4+(2𝑥)^2−2(𝑥^2 )(2𝑥) 𝒚 = 𝒙^𝟒+𝟒𝒙^𝟐−𝟒𝒙^𝟑 Differentiating w.r.t 𝑥 𝑑𝑦/𝑑𝑥=𝑑(𝑥^4 + 4𝑥^2 − 4𝑥^3 )/𝑑𝑥 𝑑𝑦/𝑑𝑥=4𝑥^3+8𝑥−12𝑥^2 𝑑𝑦/𝑑𝑥=4𝑥(𝑥^2+2−3𝑥) 𝑑𝑦/𝑑𝑥=4𝑥(𝑥^2−3𝑥+2) 𝑑𝑦/𝑑𝑥=4𝑥(𝑥^2−2𝑥−𝑥+2) 𝑑𝑦/𝑑𝑥=4𝑥(𝑥(𝑥−2)−1(𝑥−2)) 𝑑𝑦/𝑑𝑥=4𝑥((𝑥−1)(𝑥−2)) 𝑑𝑦/𝑑𝑥=4𝑥(𝑥−1)(𝑥−2) Putting 𝒅𝒚/𝒅𝒙=𝟎 4𝑥(𝑥−1)(𝑥−2)=0 So, 𝑥=0 , 𝑥=1 & 𝑥=2 Plotting points on real line Thus, the function is strictly increasing for 0 <𝒙<𝟏 and 𝒙>𝟐

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