Download App

Increasing and Decreasing Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIncreasing and Decreasing Functions1 Mark
MCQ
Function $f(x) = x^3 - 27x + 5$ is monotonically increasing when:
  • A
    $\text{x}<-3$
  • ✓
    $|\text{x}|>3$
  • C
    $\text{x}\leq-3$
  • D
    $|\text{x}|\geq3$
✓

Answer

Correct option: B.
$|\text{x}|>3$

$f(x) = 3x^2 - 27x$
$\Rightarrow f'(x) = x^3 - 27x + 5$
$\Rightarrow f'(x) = 3(x^2 - 9)$
Function is increasing,
$3\big(\text{x}^2-9\big)\geq0$
$\Rightarrow\text{x}^2\geq9$
$\Rightarrow|\text{x}|\geq3$

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

$A = [a_{ij}]_{m \times n }$ is a square matrix, if$:$
→
If $\cos^{-1}\frac{\text{x}}{2}+\cos^{-1}\frac{\text{y}}{2}=\theta,$ then $\Rightarrow9\text{x}^2-12\text{xy}\cos\theta+4\text{y}^2$ is equal to:
  1. $36$
  2. $-36\sin^2\theta$
  3. $36\sin^2\theta$
  4. $-36\cos^2\theta$
→
The sum of the squares of sine of the angles made by the line AB with OX, OY, OZ where O is the origin is:
  1. 1
  2. 2
  3. -1
  4. 3
→
The area under the curve $y= 2x^{3 }+ 4x^2$ between $x = 2, x = 4$ is:
→
If $\left|\begin{array}{lll}2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1\end{array}\right|+3=0$, then the value of $x$ is
→
What is integrating factor of $\frac{\text{dy}}{\text{dx}}+\text{y}\sec\text{x}=\tan\text{x}?$
  1. $\sec\text{x}+\tan\text{x}$
  2. $\log(\sec\text{x}+\tan\text{x})$
  3. $\text{e}^{\sec\text{x}}$
  4. $\sec{\text{x}}$ 
→
The angle between the lines $2 x=3 y=-z$ and $6 x=-y=-4 z$ is
→
If $f(x)=\left\{\begin{array}{cl}\frac{1}{1+e^{1 x}} & , x \neq 0 \\ 0 & , x=0\end{array}\right.$ then $f ( x )$ is
→
The transpose of a row matrix is:
  1. zero matrix
  2. diagonal matrix
  3. column matrix
  4. row matrix
→
Order of $\Big(\frac{\text{dy}}{\text{dx}}+3\text{x}\Big)^\frac{3}{2}=\text{x}+\frac{3\text{dy}}{\text{dx}}$ is:
  1. 3
  2. 2
  3. 1
  4. 4
→