The equation of the tangent to the conic $${x^2} - {y^2} - 8x + 2y + 11 = 0$$ at (2, 1) is

A particle is moving in a straight line. At time t, the distance between the particle from its starting point is given by x = t $$-$$ 6t² + t³. Its acceleration will be zero at

The Rolle's theorem is applicable in the interval $$-$$1 $$\le$$ x $$\le$$ 1 for the function

The distance covered by a particle in t seconds is given by x = 3 + 8t $$-$$ 4t². After 1 second its velocity will be