In which of the following intervals, the function y(x) = x3 - 3x2 - 9x + 5 is always decreasing?

Question

In which of the following intervals, the function y(x) = x3 - 3x2 - 9x + 5 is always decreasing? (A)  (-1 , 3)  (B)  (-3 , 3)  (C)  (-4 , 4)  (D)  (-2 , 2)

Tardigrade Admin · Accepted Answer

We have, y (x) =x3-3x2-9x+5 dots (i) Differentiating (i) w.r.t. x, we get y'(x)=3x2-6x-9 =(x-3)(3x+3) Now, y'(x)=0 ⇒ x=3 and -1 Sign change for y'(x) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/7d4be5dca8880d915a9d0e3d63e20a55-.jpeg" /> Hence, y(x) is decreasing in (-1, 3)

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

$(- 1, 3)$

$(- 3, 3)$

$(- 4, 4)$

$(- 2, 2)$

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

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

Q. In which of the following intervals, the function y(x)=x3−3x2−9x+5 is always decreasing?

(−1,3)

(−3,3)

(−4,4)

(−2,2)