Step 1 :Define the function \(f(t) = t - 8 \sqrt{t + 2}\).
Step 2 :Calculate the derivative of the function, \(f'(t) = 1 - \frac{4}{\sqrt{t + 2}}\).
Step 3 :Solve the equation \(f'(t) = 0\) to find the critical points.
Step 4 :The solution to the equation is \(t = 14\).
Step 5 :Check if this point is in the domain of the function. The function is defined for \(t \geq -2\). So, 14 is in the domain of the function.
Step 6 :Therefore, the function has one critical point at \(t = 14\).
Step 7 :Final Answer: The critical point of the function \(f(t)=t-8 \sqrt{t+2}\) is \(\boxed{14}\).