# Consider the given function and the given interval.f(x) = 18 sin(x) – 9 sin(2x), [0, x](a) Find the average value fave of f on the given interval.fave%3D(b) Find c such that fave = f(c). (Round your answers to three decimal places.)(smaller value)(larger value)

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Step 1

Average value fave of f(x) on the given interval [a, b] is given by -

Difference rule of integration is given by –

Step 2

Given –

a)

Substituting given values of f(x), a and b in the formula.

Using a difference rule of integration can be rewritten as

Step 3

b)               We have to find c such that favg =f(c)

Substituting x = c in f(x) we will get

So according to the question

Using graphing calculator we can find two values of c

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