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)

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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