The curve y - e^xy + x = 0 has a vertical tangent  at the point

The radius of a circle is increasing at the rate of 0.1 cm/sec.  When r = 5 cm, the rate of change of area is

If tangent to the curve x = at², y = 2at is perpendicular to x axis, then its point of contact is:

The total cost C (x )  associated with the production of x units of an item is given by C (x ) = 0.007 x³  - 0.003x² + 15x + 4000.When 17 units are produced  the marginal cost is

A man is walking at the rate of 8 kmph towards the foot of a tower 60 metres high.The rate at which he is approaching the top when he is 80 metres from the foot of the tower is.

The tangent to the parabola x² = 2 y at the point makes with x - axis at an angle

The equation of the tangent at the point  p (t), where t is any parameter, to the parabola y² = 4ax is:

The tangent of the curve x² + y² – 2x -3 = 0  is parallel to axis at the point:

If  f (x)  = x² + ax + 1  is strictly increasing on ( 1, 2 ), then the least value of a is

When r = 4cm, the rate of change of the area of a circle w.r.t its radius  r is.