Smallest Area of a Triangle Formed from the Tangent Line of a Parabola

This problem is an applied optimization problem. The problem is to minimize the area of the triangle formed by a tangent line to the function y = ¹⁄₉ x². The triangle is defined by the origin, the x-intercept of the tangent line, and the y-intercept of the tangent line. Only triangles formed in the first quadrant are of concern.