The function f(x)=3-4 x+2 x^2-1 3 x^3 is - Vidyadip

MCQ

The function $f(x)=3-4 x+2 x^2-\frac{1}{3} x^3$ is

A
increasing on $R$
✓
decreasing on $R$
C
neither increasing nor decreasing
D
none of these

✓

Answer

Correct option: B.

decreasing on $R$

(b) : $f(x)=3-4 x+2 x^2-\frac{1}{3} x^3$
$
\therefore f^{\prime}(x)=-4+4 x-x^2=-\left(x^2-4 x+4\right)=-(x-2)^2<0
$
for all $x \in R$
Thus, $f(x)$ is decreasing on $R$.

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 Application of Derivatives→Application of Derivatives — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The maximum area of a right angled triangle with hypotenuse $h$ is

If $a \ne b \ne c,$ the value of $x$ which satisfies the equation $\left| {\,\begin{array}{*{20}{c}}0&{x - a}&{x - b}\\{x + a}&0&{x - c}\\{x + b}&{x + c}&0\end{array}\,} \right| = 0$, is

Consider the matrix $f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$

Given below are two statements:

Statement I: $f(-x)$ is the inverse of the matrix $f(x)$.

Statement II: $f(x) f(y)=f(x+y)$.

In the light of the above statements, choose the correct answer from the options given below

If $y = \frac{1}{{\sqrt {{a^2} - {b^2}} }}{\cos ^{ - 1}}\left[ {\frac{{a\cos (x - \alpha ) + b}}{\theta }} \right]$ where $\theta = a + b\cos (x - \alpha )$, then $\frac{{dy}}{{dx}} = $

$f(x)=x-[x]$ in the interval $[0,1]$ is

A straight line L on the xy-plane bisects the angle between OX and OY. What are the direction cosines of L:

$\Big(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},0\Big)$
$\Big(\frac{1}{2},\frac{\sqrt{3}}{2},0\Big)$
$\big(0,0,1\big)$
$\Big(\frac{2}{3},\frac{2}{3},\frac{1}{3}\Big)$

The number of solutions of the equation
$\tan^{-1}2\text{x}+\tan^{-1}3\text{x}=\frac{\pi}{4}$ is:

2
3
1
none of these

Angle between vectors $\bar{a}=6 \hat{i}+2 \hat{j}-8 \hat{k}$ and $\bar{b}=4 \hat{i}-4 \hat{j}+2 \hat{k}$ is ___________ .

For two events $A$ and $B$, if $P(A) = P\left( {\frac{A}{B}} \right) = \frac{1}{4}$ and $P\left( {\frac{B}{A}} \right) = \frac{1}{2}$, then

If $y = {{{e^x}\log x} \over {{x^2}}}$, then ${{dy} \over {dx}} = $