Final answer:
To find the absolute minimum value of y = -cos(x) - sin(x) on the closed interval, we can differentiate the function and set the derivative equal to zero. The absolute minimum value is -√2.
Step-by-step explanation:
To find the absolute minimum value of y = -cos(x) - sin(x) on the closed interval, we can differentiate the function and set the derivative equal to zero. Taking the derivative, we get y' = sin(x) - cos(x). We set y' = 0 and solve for x to find the critical points. The critical points occur when x = 45° + nπ or x = 225° + nπ for any integer n. By substituting these values back into the original function, we can determine the corresponding y values. Comparing these values, we find that the absolute minimum value of y = -cos(x) - sin(x) on the closed interval is -√2.