Let f(x)=| |. Then, - Vidyadip

MCQ

Let $\text{f(x)}=|\cos\text{x}|.$ Then,

A
$f(x)$ is everywhere differentiable.
B
$f(x)$ is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
✓
$f(x)$ is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
D
None of these.

✓

Answer

Correct option: C.

$f(x)$ is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$

$\text{f}(\text{x)} = |\cos\text{x}|$
Given function is trigonometric function.
$\Rightarrow $ Hence, it is continuous.
Function is not differentiable at odd multiples of $\frac{\pi}{2}.$
$\Rightarrow f(x)$ is not differentiable at $\text{x} = (2\text{n} + 1) \frac{\pi}{2}$

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 Continuity and Differentiability→Continuity and Differentiability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Which of the following is a homogeneous differnetial equation?

If $f(x) = {1 \over {\sqrt {{x^2} + {a^2}} + \sqrt {{x^2} + {b^2}} }}$, then $f'(x)$ is equal to

Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+\alpha \hat{\mathrm{j}}+\beta \hat{\mathrm{k}}, \alpha, \beta \in \mathrm{R}$. Let a vector $\overrightarrow{\mathrm{b}}$ be such that the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$ and $|\vec{b}|^2=6$, If $\vec{a} \cdot \vec{b}=3 \sqrt{2}$, then the value of $\left(\alpha^2+\beta^2\right)|\vec{a} \times \vec{b}|^2$ is equal to

$\int_{}^{} {\frac{1}{{{{({e^x} + {e^{ - x}})}^2}}}\;dx = } $

${d \over {dx}}{\tan ^{ - 1}}\left( {{{ax - b} \over {bx + a}}} \right) = $

Let $f:\left[(1, \infty) \rightarrow \mathbb{R}\right.$ be a differentiable function such that $f(1)=\frac{1}{3}$ and $3 \int_1^x f(t) d t=x f(x)-\frac{x^3}{3}, x \in[1, \infty)$.

Let $e$ denote the base of the natural logarithm. Then the value of $\mathrm{f}(e)$ is

The order and the degree of differential equation $\frac{{{d^4}y}}{{d{x^4}}} - 4\frac{{{d^3}y}}{{d{x^3}}} + 8\frac{{{d^2}y}}{{d{x^2}}} - 8\frac{{dy}}{{dx}} + 4y = 0$ are respectively

If $ab + bc + ca = 0$ and $\left| {\,\begin{array}{*{20}{c}}{a - x}&c&b\\c&{b - x}&a\\b&a&{c - x}\end{array}\,} \right| = 0$, then one of the value of $x$ is

Two vectors each of magnitudes $1$ unit are inclined at $60^{\circ}$ to each other. The difference of the vectors has a magnitude $............?$

If $A, B$ are non-singular square matrices of the same order, then $\left(A B^{-1}\right)^{-1}=$