brute force methods brute force root finding assume that we have set of points along the curve of function /we want to solve xd find the points where crosses the axis brute force algorithm is to run through all points on the curve and check if one point is below the axis and if the next point is above the axisor the other way around if this is found to be the casewe know that must be zero in between these two points numerical algorithm more preciselywe have set of points xi yi /yi xi / nwhere (or the other way arounda compact expression for this check is to perform the test yi yi if sothe root of xd is in oexi xi assuming linear variation of between xi and xi we have the approximation xyi yi xi xi xi xi xi yi xi xi xi xi whichwhen set equal to zerogives the root xi xi xi yi yi yi implementation given some python implementation (xof our mathematical functiona straightforward implementation of the above numerical algorithm looks like