Question 6
y = x (x â 3)2 decreases for the values of x given by :
1 < x < 3 (B) x < 0
(C) x > 0 (D) 0 < x < 3/2
đ(đĽ)=đĽă(đĽâ3)ă^2
Calculating fâ(đ)
fâ(đĽ) = (đĽâ3)^2+đĽĂ2(đĽâ3)
fâ(đĽ) = (đĽâ3) [(đĽâ3)+2đĽ]
fâ(đĽ) = (đĽâ3) (3đĽâ3)
fâ(đĽ) = (đĽâ3) Ă3(đĽâ1)
fâ(đ) = đ(đâđ) (đâđ)
Putting fâ(đ) = 0
3(đĽâ3) (đĽâ1)=0
So, đ = 3 , 1
Plotting points on number line
Hence, f is decreasing for the đ<đ<đ.
So, the correct answer is (A)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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