Question

In which of the following intervals, the function $y(x) = x^3 - 3x^2 - 9x + 5$ is always decreasing?

• A. $(-1 , 3)$
• B. $(-3 , 3)$
• C. $(-4 , 4)$
• D. $(-2 , 2)$

Answer 1

Answer: (A)

$(-1 , 3)$

Answer 2

We have, $y (x) =x^{3}-3x^{2}-9x+5 \dots (i)$
Differentiating (i) w.r.t. x, we get
$y'(x)=3x^{2}-6x-9$
$=(x-3)(3x+3)$
Now, $y'(x)=0$
$\Rightarrow x=3$ and $-1$
Sign change for $y'{(x)}$

Hence, $y(x)$ is decreasing in $(-1, 3)$