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If $y = 8 x^{3} - 60 x^{2} + 144 x + 57$ is a decreasing function in the interval $(a, b)$ , then $(a, b)$ is

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$(- 3, 2)$

$(2, 3)$

$(5, 6)$

$(3, 2)$

answer is B.

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Detailed Solution

$f^{1} (x) < 0 24 x^{2} - 120 x + 144 < 0 \Rightarrow x^{2} - 5 x + 6 < 0 ⇒ 2 < x < 3$

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