Question 6 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by

y = x (x – 3) 2 decreases for the values of x given by :

(A)1 < x < 3  

(B) x < 0

(C) x > 0  

(D) 0 < x < 3/2

 

This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives

Slide71.JPG

Slide72.JPG
Slide73.JPG

Go Ad-free

Transcript

Question 6 y = x (x – 3)2 decreases for the values of x given by : 1 < x < 3 (B) x < 0 (C) x > 0 (D) 0 < x < 3/2 𝑓(𝑥)=𝑥〖(𝑥−3)〗^2 Calculating f’(𝒙) f’(𝑥) = (𝑥−3)^2+𝑥×2(𝑥−3) f’(𝑥) = (𝑥−3) [(𝑥−3)+2𝑥] f’(𝑥) = (𝑥−3) (3𝑥−3) f’(𝑥) = (𝑥−3) ×3(𝑥−1) f’(𝒙) = 𝟑(𝒙−𝟑) (𝒙−𝟏) Putting f’(𝒙) = 0 3(𝑥−3) (𝑥−1)=0 So, 𝒙 = 3 , 1 Plotting points on number line Hence, f is decreasing for the 𝟏<𝒙<𝟑. So, the correct answer is (A)

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