Question 19
y = x (x โ 3)2 decreases for the values of x given by :
1 < x < 3 (B) x < 0
(C) x > 0 (D) 0 < x < 3/2
๐(๐ฅ)=๐ฅใ(๐ฅโ3)ใ^2
Calculating fโ(๐)
fโ(๐ฅ) = (๐ฅโ3)^2+๐ฅร2(๐ฅโ3)
fโ(๐ฅ) = (๐ฅโ3) [(๐ฅโ3)+2๐ฅ]
fโ(๐ฅ) = (๐ฅโ3) (3๐ฅโ3)
fโ(๐ฅ) = (๐ฅโ3) ร3(๐ฅโ1)
fโ(๐) = ๐(๐โ๐) (๐โ๐)
Putting fโ(๐) = 0
3(๐ฅโ3) (๐ฅโ1)=0
So, ๐ = 3 , 1
Plotting points on number line
Hence, f is decreasing for the ๐<๐<๐.
So, the correct answer is (A)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.