Using Lagrange's mean-value theorem, find a point on the curve `y = x^(2)`, where the tangent is parallel to the line joining the points (1, 1) and (2, 4)

Using Lagrange's mena value theorem, find a point on the curve y=x^(2) where the tangent to the curve is parallel to the line joining the points (1, 1) and (2, 4).

Find a point on the curve y= (x-3)^(2) , where the tangent is parallel to the chord joining the points (3,0) and (4,1).

Find a point on the curve y = x^(3) , where the tangent to the curve is parallel to the chord joining the points (1, 1) and (3, 27)

Find a point on the curve y=(x-2)^2 at which the tangent is parallel to the chord joining the points (1,1) and (4,4)

Find a point on the curve f(x)= (x-3)^2 , where the tangent is parallel to the chord joining the points (3, 0) and (4, 1).

Find a point on the curve y=(x-3)^2 , where the tangent is parallel to the line joining (4,\ 1) and (3,\ 0) .

Find a point on the curve y=(x-3)^2 , where the tangent is parallel to the line joining (4,\ 1) and (3,\ 0) .