Find the point on the graph of the function that is closest to the point. f(x)=x² (2,1/2)

Solution:

The graph below represents the problem statement pictorially:

From the graph, it is apparent that point B(2, 1/2) does not lie on the curve. The graph also reveals that point B is closer to point C on the curve than point A (2,4).

The coordinates of point C can be found from the equation of the curve y = x^2. . The value of Y at point c is 1/2. therefore the value of x will be:

y = x²

1/2 = x²

⇒ x = 1/√2

x = 0.707

The closest point to point B (2, 1/2 ) is point C which is (1/√2, 1/2).

Find the point on the graph of the function that is closest to the point. f(x)=x² (2,1/2).

Summary:

The point on the curve closest to (2, 1/2) is the point (1/√2, 1/2).