The function f(x)=| | is: 1. Differentiable atx=(2n+1) 2 ,n 2. Co… - Vidyadip

Question

The function $\text{f(x)}=|\cos\text{x}|$ is:

Differentiable at$\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
Continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
Neither differentiable nor continuous at $\text{x}=\text{n}\in\text{Z}$
None of these.

✓

Answer

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

Solution:

$\text{f(x)}=|\cos\text{x}|$

Given function is trigonometric function.

⇒ Hence, it is continuous.

Function is not differentiable at odd multiples of $\frac{\pi}{2}$

⇒ 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 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 system of equations, $a^2 x - ay = 1 - a$ & $bx + (3 - 2b) y = 3 + a$ possess a unique solution $x = 1, y = 1$ then :

The degree of the differential equation $\text{y}_3^\frac{2}{3}+2+3\text{y}_2+\text{y}_1=0$ is:

1
2
3
none of these

The value of $b>3$ for which

$12 \int \limits_{3}^{b} \frac{1}{\left(x^{2}-1\right)\left(x^{2}-4\right)} d x=\log _{e}\left(\frac{49}{40}\right)$, is equal to

The corner points of the feasible region determined by the following system of linear inequalities:

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).

Let Z = px + qy, where p.q > 0.

Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is:

P = q
p = 2q
p = 3q
q = 3q

The vector$(s)$ which is/are coplanar with vectors $\hat{i}+\hat{j}+2 \hat{k}$ and $\hat{i}+2 \hat{j}+\hat{k}$, and perpendicular to the vector $\hat{i}+\hat{j}+\hat{k}$ is/are

$(A)$ $\hat{j}-\hat{k}$ $(B)$ $-\hat{i}+\hat{j}$ $(C)$ $\hat{i}-\hat{j}$ $(D)$ $-\hat{j}+\hat{k}$

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is:

720
120
0
None of these.

If ${\tan ^{ - 1}}x + {\tan ^{ - 1}}y + {\tan ^{ - 1}}z = \pi $, then $x + y + z$ is equal to

The solution of the equation $\frac{d y}{d x}+2 y=4 x$ is :

The corner points of the feasible region determined by the following system of linear inequalities : $2 x+y \leq 10, x+3 y \leq 15$, $x, y \geq 0$ are $(0,0),(5,0),(3,4)$ and $(0,5)$. Let $Z =p x+q y$ where $p, q>0$, condition on $p$ and $q$ so that the maximum of Z occurs at both $(3,4)$ and $(0,5)$ is

If $y = {\sin ^{ - 1}}{{2x} \over {1 + {x^2}}} + {\sec ^{ - 1}}{{1 + {x^2}} \over {1 - {x^2}}}$, then ${{dy} \over {dx}} =$