Posted by James on .
Consider the given function and the given interval.
f(x) = 4 sin x − 2 sin 2x, [0, π]
(a) Find the average value fave of f on the given interval.
fave =
(b) Find c such that fave = f(c). (Round your answers to three decimal places.)
c = (smaller value)
c = (larger value)

calculus 
Reiny,
the average value of the function is
1/(π0) ∫(4sinx  2sin 2x)dx from x = 0 to π
= (1/π) [4cosx + cos 2x] from 0 to π
= (1/π) ( 4cosπ + cos 2π  (4cos0 + cos0) )
= (1/π)( 4 + 1  (4 + 1) )
= (1/π)(8) = 8/π
b) if 4sinx  2sin 2x = 8/π
2sinx  sin 2x = 4/π
2sinx  2sinxcosx = 4/π
sinx  sinxcosx = 2/π
nasty equation to solve, I ran it through Wolfram to get
x or c = 1.238224 or c = 2.80812
http://www.wolframalpha.com/input/?i=sinx++sinxcosx+%3D+2%2Fπ