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

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  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Question 19 y = x (x โ€“ 3)2 decreases for the values of x given by : 1 < x < 3 (B) x < 0 (C) x > 0 (D) 0 < x < 3/2 ๐‘“(๐‘ฅ)=๐‘ฅใ€–(๐‘ฅโˆ’3)ใ€—^2 Calculating fโ€™(๐’™) fโ€™(๐‘ฅ) = (๐‘ฅโˆ’3)^2+๐‘ฅร—2(๐‘ฅโˆ’3) fโ€™(๐‘ฅ) = (๐‘ฅโˆ’3) [(๐‘ฅโˆ’3)+2๐‘ฅ] fโ€™(๐‘ฅ) = (๐‘ฅโˆ’3) (3๐‘ฅโˆ’3) fโ€™(๐‘ฅ) = (๐‘ฅโˆ’3) ร—3(๐‘ฅโˆ’1) fโ€™(๐’™) = ๐Ÿ‘(๐’™โˆ’๐Ÿ‘) (๐’™โˆ’๐Ÿ) Putting fโ€™(๐’™) = 0 3(๐‘ฅโˆ’3) (๐‘ฅโˆ’1)=0 So, ๐’™ = 3 , 1 Plotting points on number line Hence, f is decreasing for the ๐Ÿ<๐’™<๐Ÿ‘. So, the correct answer is (A)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.