Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Let $f left parenthesis x right parenthesis equals x c o s to the power of negative 1 end exponent invisible function application left parenthesis negative s i n invisible function application vertical line x vertical line right parenthesis comma x element of open square brackets negative fraction numerator pi over denominator 2 end fraction comma fraction numerator pi over denominator 2 end fraction close square brackets$ , then which of the following is true?

$f^{}$ '/> is increasing in $(- \frac{π}{2}, 0)$ and decreasing in $(0, \frac{π}{2})$
$f^{}$ (0)=-π2'/>
$f$ is not differentiable at $x = 0$
$f$ is decreasing in $(- \frac{π}{2}, 0)$ and increasing in $(0, \frac{π}{2})$

The correct answer is: $f$ is not differentiable at $x equals 0$

Related Questions to study

For all twice differentiable functios $f colon R rightwards arrow R$ , with $f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0$

For all twice differentiable functios $f colon R rightwards arrow R$ , with $f left parenthesis 0 right parenthesis equals f left parenthesis 1 right parenthesis equals f to the power of ´ end exponent left parenthesis 0 right parenthesis equals 0$

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $theta$ should be :–

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $theta$ should be :–

physics-General

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

A string of negligible mass going over a clamped pulley of mass m supports a block of mass M as shown in the figure. The force on the pulley by the clamp is given by :–

physics-General

parallel

Let $f$ be a twice differentiable function on $left parenthesis 1 , 6 right parenthesis$ . If $f left parenthesis 2 right parenthesis equals 8$ , $f to the power of ´ end exponent left parenthesis 2 right parenthesis equals 5 comma f to the power of ´ end exponent left parenthesis x right parenthesis greater or equal than 1$ and $f to the power of ´ left parenthesis x right parenthesis greater or equal than 4$ , for all $x element of left parenthesis 1 , 6 right parenthesis$ , then $colon$

Let $f$ be a twice differentiable function on $left parenthesis 1 , 6 right parenthesis$ . If $f left parenthesis 2 right parenthesis equals 8$ , $f to the power of ´ end exponent left parenthesis 2 right parenthesis equals 5 comma f to the power of ´ end exponent left parenthesis x right parenthesis greater or equal than 1$ and $f to the power of ´ left parenthesis x right parenthesis greater or equal than 4$ , for all $x element of left parenthesis 1 , 6 right parenthesis$ , then $colon$

A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is $1 third$ . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of $alpha$ is given :

A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is $1 third$ . If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical, the maximum possible value of $alpha$ is given :

physics-General

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, . If the coefficient of friction between the rod and bead is , and gravity is neglected, then the time after which the bead starts slipping is

A long horizontal rod has a bead which can slide along its length and is initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with a constant angular acceleration, . If the coefficient of friction between the rod and bead is , and gravity is neglected, then the time after which the bead starts slipping is

physics-General

parallel

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals $mu$ The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction $mu$ and the distance x(=QR), are, respectively close to:

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals $mu$ The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction $mu$ and the distance x(=QR), are, respectively close to:

physics-General

An observer can see through a pin–hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

An observer can see through a pin–hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is

physics-General

A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

A diverging beam of light from a point source S having divergence angle a, falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is

physics-General

parallel

A rectangular glass slab ABCD, of refractive index n₁, is immersed in water of refractive index $n subscript 2 end subscript open parentheses n subscript 1 end subscript greater than n subscript 2 end subscript close parentheses$ A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence a_max, such that the ray comes out only from the other surface CD is given by

A rectangular glass slab ABCD, of refractive index n₁, is immersed in water of refractive index $n subscript 2 end subscript open parentheses n subscript 1 end subscript greater than n subscript 2 end subscript close parentheses$ A ray of light in incident at the surface AB of the slab as shown. The maximum value of the angle of incidence a_max, such that the ray comes out only from the other surface CD is given by

physics-General

A smooth block is released at rest on a incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-

A smooth block is released at rest on a incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-

physics-General

A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-

A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-

physics-General

parallel

If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by $6 0 to the power of 0 end exponent$ , then $c o s blank B equals$

If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by $6 0 to the power of 0 end exponent$ , then $c o s blank B equals$

Two plane mirrors. A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of $30 degree$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

Two plane mirrors. A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of $30 degree$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

physics-General

A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is

A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.