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Find the absolute extrema of the function f(x)=sin x on [5 π/6, 11 π/6].

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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.

User Levi Hackwith
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