Find all critical points of the function $f(t)=t-8 \sqrt{t+2}$.
(Use symbolic notation and fractions where needed. Give your answer in the form of a comma separated list. If the funct does not have any critical points, enter DNE.)
critical points:
Answer
Final Answer: The critical point of the function \(f(t)=t-8 \sqrt{t+2}\) is \(\boxed{14}\).
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 \(\boxed{14}\).
