Question

If $y = 8x^3 - 60x^2 + 144x + 27$ is strictly decreasing function in the interval

• A. ( - 5, 6)
• B. $( −\infty , 2)$
• C. ( 5,6)
• D. $( 3, \infty )$
• E. (2,3)

Answer 1

Answer: (E)

Given, $y=8 x^{3}-60 x^{2}+144 x+27$
$\frac{d y}{d x}=24 x^{2}-120 x+144$
For function to be strictly decreasing, $\frac{d y}{d x}<0$
$\Rightarrow 24 x^{2}-120 x+144<0$
$\Rightarrow 24\left(x^{2}-5 x+6\right)<0$
$\Rightarrow \left(x^{2}-5 x+6\right)<0$
$\Rightarrow x^{2}-2 x-3 x+6<0$
$\Rightarrow x(x-2)-3(x-2)<0$
$\Rightarrow (x-3)(x-2)<0$
$\therefore x \in(2,3)$