Download App

Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
Function $f(x) = |x| - |x - 1|$ is monotonically increasing when :
  • A
    $x < 0$
  • B
    $x > 1$
  • C
    $x < 1$
  • ✓
    $0 < x < 1$
✓

Answer

Correct option: D.
$0 < x < 1$
$f(x) = |x| - |x - 1|$
Case $\text{I} :$
Let $x < 0$
If $x < 0,$ then $|x| = -x$
$\Rightarrow |x - 1| = -(x - 1)$
Now,
$f(x) = |x| - |x - 1|$
$= -x - (-x + 1)$
$= -x + x - 1$
$= -1$
$f'(x) = 0$
So, $f(x)$ is not monotonically increasing when $x < 0.$
Case $\text{II} :$
Let $x < 0 < 1$
Here,
$|x| = x$
$\Rightarrow |x - 1| = -(x - 1)$
Now,
$f(x) = |x| - |x - 1|$
$= x + x -1$
$= 2x - 1$

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

If $A=\left[a_{i j}\right]$ be a $3 \times 3$ matrix, where $a_{i j}=i-3 j$, then which of the following is false?
→
Evaluate $\begin{bmatrix}\sqrt{3}&\sqrt{2}\\-1&2\sqrt{3}\end{bmatrix}$ is:
→
If $f(x) = 3x - 5$, then ${f^{ - 1}}(x)$
→
Value of $\int\frac{\text{dx}}{\sqrt{2\text{x}-\text{x}^2}}$
→
Let $x$ denote the total number of one-one functions from a set $A$ with $3$ elements to a set $B$ with $5$ elements and $y$ denote the total number of one-one functions from the set $A$ to the set $A \times B$. Then ...... .
→
Let $\overrightarrow{ a }=2 \hat{ i }+\hat{ j }+\hat{ k }$, and $\overrightarrow{ b }$ and $\overrightarrow{ c }$ be two nonzero vectors such that $|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}| \quad$ and $\vec{b} \cdot \vec{c}=0$. Consider the following two statement:

$(A)$ $|\overrightarrow{ a }+\lambda \overrightarrow{ c }| \geq|\overrightarrow{ a }|$ for all $\lambda \in R$.

$(B)$ $\overrightarrow{ a }$ and $\overrightarrow{ c }$ are always parallel

→
If the corner points of the feasible region of an LPP are $(0,3),(3,2)$ and $(0,5)$, then the minimum value of $Z=11 x+7 y$ is
→
In a triangle $\mathrm{ABC}$, if $|\overrightarrow{\mathrm{BC}}|=3,|\overrightarrow{\mathrm{C}}|=5$ and $|\overrightarrow{\mathrm{BA}}|=7$, then the projection of the vector $\overline{\mathrm{BA}}$ on $\overline{\mathrm{BC}}$ is equal to:
→
Choose the correct answer The maximum value of $[\text{x(x}-1)+1]^\frac{1}{3},0\leq\text{x}\leq1]\text{is:}$
→
For the $LP$ problem

Maximize $z=2 x+3 y$ the coordinates of the corner points of the bounded feasible region are $A\,(3,3), B\,(20,3),$ $\mathrm{C}\,(20,10), \mathrm{D}\,(18,12)$ and $\mathrm{E}\,(12,12) .$ The maximum value of $z$ is $\ldots \ldots$

→