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)

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.