Question
Let be a twice differentiable function on . If , and , for all , then
( 5 ) ≤ 26 '/>
( 5 ) ≥ 28 '/>
( 5 ) + f ' ' ( 5 ) ≤ 20 '/>

The correct answer is:
Related Questions to study
A insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is . 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 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 . 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 is given :
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
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 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 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 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 and the distance x(=QR), are, respectively close to:
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
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
A rectangular glass slab ABCD, of refractive index n_{1}, is immersed in water of refractive index 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 n_{1}, is immersed in water of refractive index 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 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
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