Mathematics : Application of Derivatives

Find the equation of the tangent line to the curve  y = x² – 2x + 7 which is
(a) parallel to the line 2x – y + 9 = 0
(ii) perpendicular to the line 5y – 15y = 13

At what point will the tangent to the curve y = 2x³ – 15x² + 36x – 21 be parallel to x-axis ? Also, find the equations of tangents to the curve at those points.

Find the points on the curve x² + y² -2x – 3 = 0 at which the tangents are parallel to the x-axis.

Find point on the curve y = 3x² – 12x + 6 at which tangent is parallel to x-axis. Also find the equation of tangent line. 

Find out on the curve y = x² – x – 8 at which tangent is parallel to x-axis. Also find the equation of tangent line.

Find out on the curve y = 2 x² – 6x – 4 at which tangent is parallel to x-axis. Also find the equation of tangent line.

Find out the points on the curve  at which the tangents are (i) parallel to the x-axis and (ii) parallel to the y-axis.