Question 17
The interval on which the function f(π₯) = 2π₯3 + 9π₯2 + 12π₯ - 1
is decreasing is:
(A) [β1,β) (B) [β2, β1]
(C) (ββ,β2] (D) [β1, 1]
f(π₯) = 2π₯3 + 9π₯2 + 12π₯ - 1
Calculating fβ(π)
fβ(π₯) = 6π₯2 +18π₯ + 12 - 0
fβ(π₯) = 6(π₯2+3π₯+2)
fβ(π₯) = 6(π₯2+2π₯+π₯+2)
fβ(π₯) = 6(π₯(π₯+2)+1(π₯+2))
fβ(π) = 6(π+π) (π+π)
Putting fβ(π) = 0
6(π₯+1) (π₯+2) = 0
(π₯+1) (π₯+2) = 0
So, π = β1 , β2
Plotting points on number line
Hence, f is decreasing for the interval (β2, β1).
So, the correct answer is (B)

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.