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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Last updated at April 16, 2024 by Teachoo
This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives
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)