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

MCQ

Let $\text{f(x)}=|\sin\text{x}|.$ then,

A
f(x) is everywhere differentiable.
✓
f(x) is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
C
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: B.

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

$\text{f(x)}=|\sin\text{x}|$Given function is continuous and differentiable on $(2\text{n}\pi,(2\text{n}+1)\pi)$
But not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}.$
As $\sin\text{n}\pi=0$ for $\text{n}\in\text{Z}.$

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

Similar questions

If the curve a $y + x^2 = 7$ and $x^3 = y$, cut orthogonally at $(1, 1)$ then the value of a is:

The interval in which $y = x^2 e^{-x}$ is increasing is:

The function $f(x) = [x],$ where $[x]$ denotes the greatest integer function, is continuous at :

The area bounded by the $x-$ axis, the curve $y = f(x)$ and the lines $x = 1,\,x = b$ is equal to $\sqrt {{b^2} + 1} - \sqrt 2 $ for all $b > 1$, then $f(x)$ is

The length of perpendicular from the origin to the plane which makes intercepts $\frac{1}{3},\frac{1}{4},\frac{1}{5}$ respectively on the coordinate axes is:

If $a+\alpha=1, b+\beta=2$ and $\operatorname{af}(x)+\alpha f\left(\frac{1}{x}\right)=b x+\frac{\beta}{x}, x \neq 0,$ then the value of expression $\frac{ f ( x )+ f \left(\frac{1}{ x }\right)}{ x +\frac{1}{ x }}$ is ..... .

Let $f ( x )$ and $g ( x )$ be two real polynomials of degree $2$ and $1$ respectively. If $f ( g ( x ))=8 x ^{2}-2 x$, and $g(f(x))=4 x^{2}+6 x+1$, then the value of $f(2)+g(2)$ is

$\int(3\text{x}^2-1)\text{dx} :$

The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is:

If two coins are tossed $5$ times, then the probability of getting $5$ heads and $5$ tails is