Let A represent the average value fo the function f(x) on the interval [0,6]. Is there a value of c for which the average value of f(x) on the interval [0,c] is greater than A? Why or why not?
I really hv no idea how to do this problem. Looking at the graph, I thot that there is a value of c because at x=7 the area is greater than x=6? but that's totally just a guess
Your reasoning is fine. For any , the average will be smaller since either more points will be below the maximum (for ) or the maximum will be lower (for ).
You could make this a bit more formal, but I think a simple explanation is probably all that the question is after.