Download App

STD 12 - 6. Application of derivatives — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 6. Application of derivatives1 Mark
MCQ
For all real values of  $x$ , increasing function  $f(x)$  is
  • A
    ${x^{ - 1}}$
  • B
    ${x^2}$
  • ✓
    ${x^3}$
  • D
    ${x^4}$
✓

Answer

Correct option: C.
${x^3}$
c
(c) Since $f(x) = {x^3} \Rightarrow f'(x) = 3{x^2},$

which is non-negative for all real values of $ x.$

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

Let $A=\left[a_{i j}\right]$ be a $3 \times 3$ matrix, where

$a_{i j}= 1 , \quad\quad\text { if } i=j$

$\quad\quad-x ,\quad \text { if }|i-j|=1$

$\quad\quad2 x+1, \text { otherwise }$

Let a function f: $\mathrm{R} \rightarrow \mathrm{R}$ be defined as $\mathrm{f}(\mathrm{x})=\operatorname{det}(\mathrm{A})$. Then the sum of maximum and minimum values of $f$ on $R$ is equal to:

→
If $\theta = {\sin ^{ - 1}}x + {\cos ^{ - 1}}x - {\tan ^{ - 1}}x,x \ge 0$, then the smallest interval in which $\theta $ lies is given by
→
The differential coefficient of ${\cos ^{ - 1}}\left\{ {\sqrt {{{1 + x} \over 2}} } \right\}$ with respect to $x$ is
→
Let $f : N \rightarrow R$ be a function such that $f(x+y)=2 f(x) f(y)$ for natural numbers $x$ and $y$. If $f(1)=2$, then the value of $\alpha$ for which

$\sum \limits_{k=1}^{10} f(\alpha+k)=\frac{512}{3}\left(2^{20}-1\right)$ holds, is

→
If $y = {\tan ^{ - 1}}\left( {{{\sqrt a - \sqrt x } \over {1 + \sqrt {ax} }}} \right)$, then ${{dy} \over {dx}} = $
→
If $\theta$ be the angle between the unit vectors $ a$  and $b$, then $\cos \frac{\theta }{2} = $
→
If A is a singular matrix, then adj A is:
→
If the two lines $l_{1}: \frac{ x -2}{3}=\frac{ y +1}{-2}, z =2$ and $l_{2}: \frac{x-1}{1}=\frac{2 y+3}{\alpha}=\frac{z+5}{2}$ perpendicular, then an angle between the lines $l_{2}$ and $l_{3}: \frac{1- x }{3}=\frac{2 y -1}{-4}=\frac{ z }{4}$ is
→
Primitive of $f (x) = x\,\cdot\,{2^{\ln \,({x^2} + 1)}}$ $w.r.t. x$ is
→
The number of matrices $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, where a $, b, c, d \in\{-1,0,1,2,3, \ldots \ldots, 10\}$, such that $A=A^{-1}$, is
→