y = x (x β 3) 2 decreases for the values of x given by :
(A)1 < x < 3 Β
(B) x < 0
(C) x > 0 Β
(D) 0 < x < 3/2
Β
This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives


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Last updated at Dec. 4, 2021 by Teachoo
Β
This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives
Question 19 y = x (x β 3)2 decreases for the values of x given by : 1 < x < 3 (B) x < 0 (C) x > 0 (D) 0 < x < 3/2 π(π₯)=π₯γ(π₯β3)γ^2 Calculating fβ(π) fβ(π₯) = (π₯β3)^2+π₯Γ2(π₯β3) fβ(π₯) = (π₯β3) [(π₯β3)+2π₯] fβ(π₯) = (π₯β3) (3π₯β3) fβ(π₯) = (π₯β3) Γ3(π₯β1) fβ(π) = π(πβπ) (πβπ) Putting fβ(π) = 0 3(π₯β3) (π₯β1)=0 So, π = 3 , 1 Plotting points on number line Hence, f is decreasing for the π<π<π. So, the correct answer is (A)