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
You tell us, average value of a functionOriginally Posted by chukie
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 guesson a generalized interval
is given by
...Now think, graphically will there be a point
such that
?
You tell us, average value of a function
umm no there isnt a value of c? because at x=6 it's already at a maximum? im not sure if im thinking in the right direction
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.
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