MonotonicityHard

Question

In which of the following intervals f(x) = 2x3 - 15x2 + 36x + 1 is monotonic decreasing -

Options

A.(-∞, 2)
B.(3, ∞)
C.(0 , 3)
D.(2, 3)

Solution

f(x) = 2x3 - 15x2 + 36x + 1 is monotonic decreasing if f′(x) < 0
6x2 - 30x + 36 < 0
x2 - 5x + 6 < 0
x (2, 3)

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