MonotonicityHard
Question
If y = 8x3 - 60x2 + 144x + 27 is decreasing function in the interval (a, b) then (a, b) is-
Options
A.(-3, 2)
B.(2, 3)
C.(5, 6)
D.(-3, 2)
Solution
y = 8x3 - 60x2 + 144x + 27
is a decreasing function
= 24x2 - 120x + 144 < 0
x2 - 5x + 6 < 0
(x - 3) (x - 2) < 0
x ∈ (2, 3)
is a decreasing function
= 24x2 - 120x + 144 < 0x2 - 5x + 6 < 0
(x - 3) (x - 2) < 0
x ∈ (2, 3)
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