Find the point on the parabola y=x 2 that is the closest to the point (1,2) in t

Question

Find the point on the parabola y=x 2 that is the closest to the point (1,2) in the cartesian plane. To do so, follow the steps below. Find the function f=f(x) whose minimize x gives the point on the current y=x 2 closest to (1,2). [Hint: write down the square of the distance of a point (x, y) to point (1,2), and substitute the curve y=x2 into the formula.] Find the critical point of the function f. For each critical point of f, determine whether it is a minimum or maximum. Which of the critical point gives the global minimum ? Give the coordinates (x,y) of the point on the parabola that is closest to (1,2).

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