Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=x+\sin x$ is
  • ✓
    always increasing
  • B
    always decreasing
  • C
    increasing for certain range of $x$
  • D
    None of these
✓

Answer

Correct option: A.
always increasing
(a) : $\because f(x)=x+\sin x$
Differentiating w.r.t. $x$, we get $f^{\prime}(x)=1+\cos x$
$f^{\prime}(x) \geq 0$ for all values of $x$
$(\because \cos x$ is lying between -1 to 1 )
$\therefore f(x)$ is always increasing.

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

In $( - 4,\,4)$ the function $f(x) = \int\limits_{ - 10}^x {({t^4} - 4){e^{ - 4t}}dt} $ has
→
The possible number of different orders that a matrix can have when it has $24$ elements, is :
→
The global maximum value of

$f(x) = log_{10}(4x^3 -12x^2 + 11x -3)$, $x \in \left[ {2,3} \right]$, is

→
If $\vec{\text{a}}.\hat{\text{i}}=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}\big)=\vec{\text{a}}.\big(\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}\big)=1.$then $\vec{\text{a}}=$
→
Let $f : (4, 6) \to (6,8)$ be a function defined by $f(x) = x + [\frac{x}{2}]$ (where $[.]$ denotes the greatest integer function) , then $f^{-1} (x)$ is euqal to
→
Let $R$ be the relation on the set $R$ of all real numbers defined by $a \ R \ b$ if $|a - b| \le 1$. Then $R$ is
→
$\int_0^\pi {\frac{{dx}}{{1 + \sin x}}} = $
→
Let $f$ be a real-valued differentiable function on $R$ (the set of all real numbers) such that $f(1)=1$. If the $y$ intercept of the tangent at any point $P(x, y)$ on the curve $y=f(x)$ is equal to the cube of the abscissa of $P$, then the value of $f(-3)$ is equal to
→
If $\text{y}=\text{x}^{\text{n}-1}\log\text{x}\ \text{x}^2\text{y}_2+(3-2\text{n})\text{xy}_1$ is equals to :
→
The length of the side of a square sheet of metal is increasing  at the rate of $4cm/\sec $. The rate at which the area of the sheet is increasing when the length of its side is $2\, cm$, is ........ $c{m^2}/\sec $.
→