Find the point on the parabola `y^(2) = 2x` which is closest to the point (1, 4)

Explanation

To find the point on the parabola \( y^2 = 2x \) that is closest to the point \( (1, 4) \), we can follow these steps:

### Step 1: Define the Distance Function
We need to minimize the distance between a point \( A(x, y) \) on the parabola and the point \( B(1, 4) \). The distance \( d \) is given by the formula:
\[ d = \sqrt{(x - 1)^2 + (y - 4)^2} \]
However, to simplify our calculations, we will minimize the square of the distance \( d^2 \):
...