Consider `f(x)=int_1^x(t+1/t)dt` and `g(x)=f'(x)` If P is a point on the curve `y=g(x)` such that the tangent to this curve at P is parallel to the chord joining the point `(1/2,g(1/2))` and `(3,g(3))` of the curve then the coordinates of the point P

Consider f(x) = int_(1)^(x)(t + 1t)dt and g(x) = f'(x) for x in [1/2, 3] .If P is a point on the curve y = g(x) such that the tangent to curve at P is parallel to a chord joining the points (1/2, g(1/2)) and (3,g(3)) of the curve, then if ordinate of point P is lambda then sqrt(6) lambda is equal to:

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 the points on the curve y=x^3-3x , where the tangent to the curve is parallel to the chord joining (1,\ -2) and (2,\ 2)

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

At what point is the tangent to the curve f(x)=log x parallel to the chord joining the points A(1, 0) and B(e, 1) ?

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 the points on the curve y=x^(3)-3x at which the tangents are parallel to the chord joining the points (1,-2) and (2,2) .

Determine the point on the curve y = ln x, at which the tangent will be parallel to the chord joining the points P(1,0) and Q(e, 1).