The points(s) on the curve y³ + 3x² = 12y where the tangent is vertical is(are)

The equation of the common tangent to the curves y² = 8x and xy = –1 is 

If a, b > 0 then the minimum value of  

The curve y = ax³ + bx² + cx + 8 touches x – axis at P(–2, 0) and cuts they – axis at a point Q where its gradient is 3. The value of a, b, c are respectively

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

The tangent to the curve 

At the point corresponding to  is

The points of contact of the vertical tangents to x = 2 – 3 sinθ,  y = 3 + 2 cos θ are

 the in this interval

The set of all values of a for which the function

decreases for all real x is

The length of a longest interval in which the function 3 sin x – 4Sin³x is increasing is