Optimization intuition: Worked example
Here’s an example: we’ll consider the region R, which iS a triangle. The vertice of this triangle is (2, 2). The function f(x, y) = 2x – x2 – y is then applied to each point in the region. Our goal is to find the maximum of this function on the region R. To do so, we will compute its gradient, compute x its x and y derivatives, and identify all of its critical points. Let us proceed to the task of finding the critical points. To do so, we must first find the x derivative and y derivative by using the formula x’ = 2-2x and y’ = -1. To find the critical points, we must set both derivatives equal to 0. 1 The equation 0 = 1 has no real solutions, so you cannot choose x and y to make it true. [Graph]
