average value of a function

Question

could someone walk me through how to do this type of problem?

find the two values of c in (-pi/4, pi/4) such that f(c) is equal to the average value of f(x) = 2cos*2x) on (-pi/4, pi/4)

Answer 1

desmos.com/calculator/dknmvvghjx

The above graph has the correct settings for the values of a an b (a less than b), but that did not change the average value of the function (can you tell why?).