Final answer:
To find the absolute extrema of the function f(x) = sin x on the interval [5 π/6, 11 π/6], evaluate the function at the endpoints and any critical points in between. The absolute maximum value is √3/2 at x = 5 π/6 and the absolute minimum value is -√3/2 at x = 11 π/6.
Step-by-step explanation:
To find the absolute extrema of the function f(x) = sin x on the interval [5 π/6, 11 π/6], we need to evaluate the function at the endpoints of the interval and any critical points in between.
Since the function is periodic with a period of 2π, we can ignore any multiples of 2π when evaluating the endpoints. The endpoints of the interval [5 π/6, 11 π/6] are 5 π/6 and 11 π/6.
Evaluating the function at these endpoints:
- f(5 π/6) = sin(5 π/6) = √3/2
- f(11 π/6) = sin(11 π/6) = -√3/2
Since the function only takes values between -1 and 1, the absolute maximum value is √3/2 at x = 5 π/6 and the absolute minimum value is -√3/2 at x = 11 π/6.