Download App

Increasing and Decreasing Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIncreasing and Decreasing Functions1 Mark
Question
If the function $\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$ is:
  1. Increasing.
  2. Decreasing.
  3. Constant.
  4. None of these.
✓

Answer

  1. Increasing.
Solution:
$\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$
$\therefore\ \text{f}'(\text{x})=\frac{-1}{2}+\cos\text{x}$
$\Rightarrow\text{f}'(\text{x})\geq0,\forall\ \text{x}\in\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$
$\Big[\because\ \text{for }\text{x}\in\Big[\frac{-\pi}{3},\frac{-\pi}{3}\Big],\cos\geq\frac{1}{2}\Big]$
Hence, the given function is 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 Increasing and Decreasing Functions→Increasing and Decreasing Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $A=\left[\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1\end{array}\right]$, then find $(\operatorname{adj} A)^{-1}$.
→
Choose the correct answer from the given four options.
Family $\text{y}=\text{A}\text{x}+\text{A}^3$ of curves will correspond to a differential equation of order:
  1. 3
  2. 2
  3. 1
  4. Not defined
→
If $4a + 2b + c = 0,$ then the equation $3ax^2+ 2bx + c = 0$ has atleast one real root lying in the interval:
→
Refer to Question 18 maximum of Z occurs at:
  1. (5, 0)
  2. (6, 5)
  3. (6, 8)
  4. (4, 10)
→
Maximize Z = 6x + 4y, subject to $\text{x}\leq2,\text{x}+\text{y}\leq3,-2\text{x}+\text{y}\leq1,\text{x}\geq0,\text{y}\geq0.$
  1. 12 at (2, 0)
  2. 16 at (2, 1)
  3. $\frac{140}{3}$ at $\Big(\frac{2}{3},\frac{1}{3}\Big)$
  4. 4 at (0, 1)
→
If $\text{y}=\Big(1+\frac{1}{\text{x}}\Big)^\text{x},$ then $\frac{\text{dy}}{\text{dx}}=$
  1. $\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big(\text{x}+\frac{1}{\text{x}}\Big)-\frac{1}{\text{x}+1}$
  2. $\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\log\Big(1+\frac{1}{\text{x}}\Big)$
  3. $\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big\{\log(\text{x}+1)-\frac{\text{x}}{\text{x}+1}\Big\}$
  4. $\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big\{\log\Big(\text{x}+\frac{1}{\text{x}}\Big)-\frac{1}{\text{x}+1}\Big\}$
→
The distance of the line $\vec{\text{r}}=2\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}+\lambda(\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}})$ from the plane $\vec{\text{r}}.(\hat{\text{i}}+5\hat{\text{j}}+\hat{\text{k}})=5$ is:
→
If the constraints in a linear programming problem are changed
  1. the problem is to be re-evaluated
  2. solution is not defined
  3. the objective function has to be modified
  4. the change in constraints is ignored
→
The linear programming problem minimize Z = 3x + 2y subject to constraints $s x+y \geq 8,3 x+5 y \leq 15, x \geq 0$ and $y \geq 0$, has
→
The value of $\int_{-\pi / 2}^{\pi / 2}\left(x^3+x \cos x+\tan 5 x+1\right) d x$ is
→