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

Last updated at Dec. 16, 2024 by Teachoo

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

Transcript

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

    3. NCERT Exemplar - MCQs

    Tangents and Normals (using Differentiation) →
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Chapter 6 Class 12 Application of Derivatives
Serial order wise

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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