Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The function $f(x)=\tan x-x$
  • ✓
    always increases
  • B
    always decreases
  • C
    never increases
  • D
    sometimes increases and sometimes decreases.
✓

Answer

Correct option: A.
always increases
(a) : $f(x)=\tan x-x$
$
\Rightarrow f^{\prime}(x)=\sec ^2 x-1=\tan ^2 x
$
$\tan ^2 x$ is always +ve, so $f^{\prime}(x)>0 \therefore f(x)$ always increases.

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 value of the integral $\sum\limits_{k = 1}^n {\int_0^1 {f(k - 1 + x)\,dx} } $ is
→
The volume of a sphere is increasing at $3\ cm^3/ \sec$. The rate at which the radius increases when radius is $2\ cm$, is :
→
If $I(x)=\int e^{\sin ^2 x}(\cos x \sin 2 x-\sin x) d x \quad$ and $I(0)=1$, then $I\left(\frac{\pi}{3}\right)$ is equal to
→
A pair has two children. If one of them is boy, then the probability that other is also a boy, is
→
If $a = - 3i + 7j + 5k,$ $b = - 3i + 7j - 3k$, $c = 7i - 5j - 3k$ are the three coterminous edges of a parallelopiped, then its volume is
→
$\int_{}^{} {\frac{1}{{{{\cos }^2}x{{(1 - \tan x)}^2}}}dx = } $
→
If $A = \left[ {\begin{array}{*{20}{c}}0&1&{ - 2}\\{ - 1}&0&5\\2&{ - 5}&0\end{array}} \right]$, then
→
Three integers are chosen at random from the first $20$ integers. The probability that their product is even is,
→
$Q^+$ denote the set of all positive rational numbers. If the binary operation $\text{a }\odot$ on $Q^+$ is defined as: $\text{a }\odot=\frac{\text{ab}}{2}$, then the inverse of $3$ is:
→
Which of the following is a homogeneous differential equation?
→