Optimization 1. Let a, b be non-zero. Find the point on the graph of y = ax + b which is closest to the origin. It is sufficient to minimize the square of the distance from (x, y) on the graph to (0, 0).

2. Consider a rectangle inscribed in an isosceles right triangle with opposite vertices at the right-angle and the hypotenuse. Demonstrate that the rectangle has maximal area when it is square.