First slide

Monotonicity

Question

$y = 8 x^{3} - 60 x^{2} + 144 x + 27$ is a decreasing function in the interval

Moderate

A

$[- 3, - 2]$
B

$[2, 3]$
C

$[1, 5]$
D

$[- 3, 2]$

Solution

$y = 8 x^{3} - 60 x^{2} + 144 x + 27 \frac{d y}{d x} = 24 x^{2} - 120 x + 144 f o r d e c r e a \sin g \frac{d y}{d x} < 0 x^{2} - 5 x + 6 < 0 (x - 2) (x - 3) < 0 2 < x < 3$

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