please help

Find the point on the parabol x that is closest to the point (5, 20]. Solution The distance between the point (5, 20) and the point (x, v) is "= (x - 5]? + (x - 20). (San the graph below.) 20- (X, yI O 10 15 20 25 -10 Out it (x, y) lies on the parabola, then x - . so the expression for it brenmes d = (72 5) ( 20). (Alternatively, we could have substituted y - v 10x to get of in terms of x alone.)=instead of minimizing 4, we minimize its square. ( You should convince yourself that the minimum of d occurs at the same point as the minimum of 92, brew is easier to work with.) Note that there is no restriction on y, so the domain is all real numbers. Differentiating, we obtain the following. )+ 2(x - 20) so " (v) = 0 when y = | - Observe that fly?