Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.)\[ f(x)=\frac{1}{x^{2}+6 x+11}\] Absolute maximum value: at \( x=\)(Enter your answers as a comma-separated list if there are multiple \( x \)-values.) Absolute minimum value: at \( x=\)(Enter your answers as a comma-separated list if there are multiple \( x \)-values.) Complete the following parts. (a) The domain of the function \( f \) is .(Enter your answer using interval notation.)(b) To determine the absolute extreme values of the function \( f \), we need the critical numbers of --- Select---\(\checkmark \).(c) To find these critical numbers, we need to find \(\mid=\).(Express your answer as a single fraction. Use positive exponents only.) exist, enter DNE.)\[ x=\](e) The Closed Interval Optimal Test ---Select-be used to find the absolute maximum value and the absolute minimum value of the function.