To find the stationary point, we first differentiate \(f(x)\) with respect to \(x\):

\(f'(x) = \frac{d}{dx}[8 - (x - 2)^2] = -2(x - 2)\)

Set the derivative equal to zero to find the stationary point:

\(-2(x - 2) = 0\)

Solving for \(x\), we get:

\(x = 2\)

Substitute \(x = 2\) back into the original function to find the \(y\)-coordinate:

\(f(2) = 8 - (2 - 2)^2 = 8\)

Thus, the coordinates of the stationary point are \((2, 8)\).

To determine the nature of the stationary point, consider the second derivative:

\(f''(x) = \frac{d}{dx}[-2(x - 2)] = -2\)

Since \(f''(x) < 0\), the stationary point at \((2, 8)\) is a maximum.