related to R studio

(d) In your own words, explain why grid search works for any function. Draw a picture to illustrate your logic. Also, does grid search become more accurate as the size of the interval shrinks to zero? Why? To apply grid search with multiple dimensions and constraints, let h(x, y) be the func- tion we seek to maximize and let k(r, y) = 0 be our constraint. First divide up the Cartesian plane into small squares. The the collection of bottom-left corners of the squares is the collection of (,y) start-points. The problem is that not all of these points satisfy the constraint. We thus throw away points that do not approximately satisfy the constraint and evaluate h(x,y) on the points that are leftover. That is, we conduct the grid search by evaluating h(I,y) on the following set of start points, {(1, y) {a, a +0.01, a +0.02, ,6 -0.01, b}{|k(x, y) =0}. We then sort the results and select the start-point (x*,y*) that leads to the largest value of f. Typically, three decimal places are used when determining if k(x,y) = 0, i.e., if k(x,y)- 0 (-0.0009, 0.0009]