On the curve `x^3=12y` the abscissa changes at a faster rate than the ordinate then y belongs to the interval

The tangent to the parabola y=x^2 has been drawn so that the abscissa x_0 of the point of tangency belongs to the interval [1,2]. Find x_0 for which the triangle bounded by the tangent, the axis of ordinates, and the straight line y=x0 2 has the greatest area.

A point is moving along the curve x^(3) = 12y, which of the coordinates changes at a faster rate at x= 10 ?

At any point on the curve 2x^2y^2-x^4=c , the mean proportional between the abscissa and the difference between the abscissa and the sub-normal drawn to the curve at the same point is equal to (a) ordinate (b) radius vector (c) x-intercept of tangent (d) sub-tangent

A particle moves along the curve 6y = x^(3) +2. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate.

Find the area bounded by the x-axis, part of the curve y=(1+8/(x^2)) , and the ordinates at x=2a n dx=4. If the ordinate at x=a divides the area into two equal parts, then find adot

A particle moves along the curve y^(2) = 8x . At what point on the curve do the abscissa and ordinate increase at the same rate?

Find the equation of a curve passing through the point (0,1).If the slope of the tangent to the curve at any point (x,y) is equal to the sum of the x coordinate(abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.

A particle moves along the curve y=2/3x^3 . Find the points on the curve at which the y-coordinate is changing twice as fast as the x-coordinate.

Find the area bounded by the curve y^(2) = 4x the x-axis and the ordinate at x=4

Using Lagrange's mean value theorem, find a point on the curve y=sqrt(x-2) defined in the interval [2, 3] where the tangent to the curve is parallel to the chord joining the end points of the curve.