The Tangent To The Graph Of The Function y = f (x) At The Point With Abscissax = 1 Form An Angle Of π/6 And At The Point x = 2 An Angle Of π/3 And At The Point x = 3 An Angle Of π/4. The Value Of                            

If the rate of change of volume of a sphere is the same as rate of change of its radius, then radius, is equal to

A spherical balloon is pumped at the constant rate of 3 m³/min. The rate of increase of its surface area as certain instant is found to be 5 m²/min. At this instant it’s radius is equal to

The third derivative of a function f’’(x) vanishes for all x. If f (0) = 1, f’ (1) = 2 and f’’ = –1, then f (x) is equal to 

The chord joining the points where x = p and x = q on the curve y = ax² + bx + c is parallel to the tangent at the point on the curve whose abscissa is 

If the tangent at (1, 1) on y² = x (2 – x)² meets the curve again at P, then P is

The distance between the origin and the normal to the curve

y = e^2x + x² at x = 0 is

If the line ax + by + c = 0 is a normal to the curve xy = 1 then

The point of intersection of the tangents drawn to the curve x²y = 1 – y at the points where it is meet by the curve xy = 1 – y is given by

The slope of the normal at the point with abscissa x = –2 of the graph of the function f (x) = | x² – x | is

The equations of the tangents to the curve y = x⁴ from the point (2, 0) not on the curve, are given by