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Calculus › Derivatives › Average rate and average value

Average value of a trigonometric function

University · ●●●○○ 50 pts

Consider the function f(x)=4sin⁡x−2sin⁡2xf(x) = 4\sin x - 2\sin 2x on the interval [0,π][0, \pi]. (a) Find the average value favef_{\text{ave}} of ff on this interval. (b) Find the two values c1<c2c_1 < c_2 in [0,π][0, \pi] such that f(c1)=f(c2)=favef(c_1) = f(c_2) = f_{\text{ave}}. Round your answers to three decimal places.

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