Download App

APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
MCQ
The function $\text{f(x)}=\tan\text{x}-\text{x}$
  • A
    Always increases.
  • B
    Always decreases.
  • C
    Never increases.
  • D
    Sometimes increases and sometimes decreases.
✓

Answer

  1. Always increases.

Solution:

We have, $\text{f(x)}=\tan\text{x}-\text{x}$

$\therefore\ \text{f}'(\text{x})=\sec^2\text{x}-1$

Since, $\text{f}'(\text{x})>0,\forall\text{ x}\in\text{R}$

Hence, 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 area bounded by the parabola x = 4 - y2 and y-axis, in square units, is:
  1. $\frac{3}{32}$
  2. $\frac{32}{3}$
  3. $\frac{33}{2}$
  4. $\frac{16}{3}$
→
If $A=\left[a_{i j}\right]=\left[\begin{array}{cc}2 & -1 \\ -3 & 4 \\ 1 & 2\end{array}\right]$ and $B=\left[b_{i j}\right]=\left[\begin{array}{ccc}2 & 3 & -5 \\ 1 & 4 & 9 \\ 0 & 7 & -2\end{array}\right]$, then value of $a_{11} b_{11}+a_{22} b_{22}$ is
→
The area of the region bounded by the curve $y = x^3,$ and the lines, $y = 8,$ and $x = 0,$ is
→
The value of $\begin{vmatrix}5^2&5^3&5^4\\5^3&5^4&5^5\\5^4&5^5&5^6\end{vmatrix}$ is:
  1. 52
  2. 0
  3. 513
  4. 59
→
If $f(x)\, = \,\left\{ {\begin{array}{*{20}{c}}{x{e^{ - \,\left( {\frac{1}{{|\,x\,|}}\, + \,\frac{1}{x}} \right)}},}&{x \ne 0}\\{0\,\,\,\,\,\,\,\,\,\,\,\,\,,}&{x = 0}\end{array}} \right.$ , then $f(x)\,$ is
→
The projection of the join of the two points (1, 4, 5), (6, 7, 2) on the line whose d.ss are (4, 5, 6) is:

  1. $\frac{17}{\sqrt{77}}$

  2. $\frac{7}{6}$

  3. $21$

  4. $\frac{7}{9}$

→
$\mathop {Lim}\limits_{n \to \infty } $$\frac{\pi }{{2\,n}}\,\,\left( {1\,\, + \,\,\cos \,\frac{\pi }{{2\,n}}\,\, + \,\,\cos \,\frac{{2\,\pi }}{{2\,n}}\,\, + \,\,.....\,\, + \,\,\cos \,\frac{{(n\, - \,1)\,\pi }}{{2\,n}}} \right)$ equal to
→
The function f(x) = 2x3 - 3x2 - 12x + 4, has:
→
If $\vec{\text{a}}$ is a non-zero of magnitude 'a' and $\lambda$ is a non-zero scalar, then $\lambda\vec{\text{a}}$ is a unit vector if:
  1. $\lambda=1$
  2. $\lambda=-1$
  3. $\text{a}=|\lambda|$
  4. $\text{a}=\frac{1}{|\lambda|}$
→
Evaluate: $\int \sec ^2(7-4 x) d x$
→