Find the points on the curve y = x³ at which the slope of the tangent is equal to y-coordinate of the point.

Find the point on the curve y = x³ – 11x + 5 at which the equation of tangent is y = x – 11.
Find the points on the curve y = x³ – 3x² – 9x + 7 at which the tangent to the curve is parallel to the x-axis.
Find the points on the curve x² + y² – 2x – 3 = 0 at which tangent is parallel to x-axis.
Find the slope of tangent to the curve y = 3x² – 6 at the point on it whose x-coordinate is 2.
Find the equations of the normal to the curve x² = 4y which passes through the point (1, 2).
Solve the differential equation = 2 cos x, given that y = 0 when
Let = , = , and = Find a vector of magnitude 6 units,which is parallel to the vector .
Find the equation of tangent to the curve at the point, where it cuts the x-axis.
Solve the differential equation : given that when x = 0, y =
If y(x) is a solution of the differential equation then find the value of
Show that the relation S in the set R of real numbers defined as S = {(a, b) : a, b ∈ R and a ≤ b³} is neither reflexive nor symmetric nor transitive.