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