The function y = 2 x^3 - 9 x^2 + 12x - 6 is monotonic decreasing,… - Vidyadip

MCQ

The function $y = 2{x^3} - 9{x^2} + 12x - 6$ is monotonic decreasing, when

✓
$1 < x < 2$
B
$x > 2$
C
$x < 1$
D
None of these

✓

Answer

Correct option: A.

$1 < x < 2$

a
(a) Here $f(x) = y = 2{x^3} - 9{x^2} + 12x - 6$

$ \Rightarrow $$f'(x) = 6{x^2} - 18x + 12$

Since$f(x)$ is increasing or decreasing in $(a,b)$ according as $f'(x) > 0$ or $ < 0$ for every $x \in (a,b)$.

Hence $f'(x) = 6(x - 2)(x - 1)$ which is obviously decreasing if $x \in (1,2)\,\,\,i.e.,\,1 < x < 2$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 6. Application of derivatives→STD 12 - 6. Application of derivatives — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $f(x) = {(a - {x^n})^{1/n}},$ where $a > 0$ and $n$ is a positive integer, then $f[f(x)] = $

The equation of normal to the curve $3x^2 - y^2 = 8$ which is parallel to the line $x + 3y = 8$ is:

Let $\{x\}$ and $[x]$ denote the fractional part of $x$ and the greatest integer $\leq x$ respectively of a real number $x$. If $\int \limits_{0}^{n}\{x\} d x, \int \limits_{0}^{n}[x] d x$ and $10\left( n ^{2}- n \right),( n \in N , n >1)$ are three consecutive terms of a $G.P.$, then $n$ is equal to

The equation of the normal to the curve $x = a \cos^3 \theta , y = a \sin^3 \theta$ at the point $\theta=\frac{\pi}{4}$ is:

If $\vec{a}, \vec{b}, \overrightarrow{ c }$ are three non-zero vectors and $\hat{ n }$ is a unit vector perpendicular to $\vec{c}$ such that $\overrightarrow{ a }=\alpha \overrightarrow{ b }-\hat{ n },(\alpha \neq 0) \quad$ and $\quad \overrightarrow{ b } \cdot \overrightarrow{ c }=12$, then $|\overrightarrow{ c } \times(\overrightarrow{ a } \times \overrightarrow{ b })|$ is equal to :

Minimise $\text{Z}=\sum\limits^{\text{n}}_{\text{j}=1}\sum\limits^{\text{m}}_{\text{i}=1}\text{c}_{\text{ij}}\cdot\text{x}_{\text{ij}}$ Subject to $\sum\limits^{\text{m}}_{\text{i}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,....\text{n}$ $\sum\limits^{\text{n}}_{\text{j}=1}\text{x}_{\text{ji}}=\text{b}_{\text{j}},\text{j}=1,2,.....,\text{m}$ is a $\ce{LPP}$ with number of constraints.

If $a = (1,\,\, - 1,\,\,1)$ and $c = ( - 1,\,\, - 1,\,\,0),$ then the vector $b$ satisfying $a \times b = c$ and $a\,\,.\,\,b = 1$ is

Let $S = \left\{ {\left( {\begin{array}{*{20}{c}}
{{a_{11}}}&{{a_{12}}}\\
{{a_{21}}}&{{a_{22}}}
\end{array}} \right):{a_{ij}} \in \left\{ {0,1,2} \right\},{a_{11}} = {a_{22}}} \right\}$ Then the number of non-singular matrices in the set $S$ is

The straight line $\frac{\text{x}-3}{3}=\frac{\text{y}-2}{1}=\frac{\text{z}-1}{0}$ is:

If $\vec a \,$ and $\vec b \,$ are non-collinear vectors, then the value of $\alpha $ for which the vectors $\vec u = \left( {\alpha - 2} \right)\vec a \, + \vec b $ and $\,\vec v = \left( {2 + 3\alpha } \right)\vec a \, - 3\vec b $ are collinear is :