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hmm, have you learned about integrals and areas under the curve yet?
if not, then I'll see if there's another way
well, I'm not sure. If so, I don't remember
you can use the area of a triangle formula A = b*h/2 and the area of a trapezoid formula A = h*(b1+b2)/2
what does area have to do with the absolute maximumt hough?
the area represents the net change notice how much of the areas are below the x axis. This means we have negative net change (ie the function is decreasing) the only area that is above the x axis is the pink triangle on the very right the question is: is the overall net change positive? or is it negative?
the net change will help us figure out where the absolute max is
ah, I see where you're getting....The overall net change would be negative.
yes, so this means that we start up somewhere high, we decrease, then come back up (like described in the last post) the overall net change is negative, so our starting point is higher than our ending point this means that the starting point is our abs max
That makes sense. So the absolute maximum is at x = -2
sure we have an increasing interval on 5 < x < 6 but this increase is not enough to go higher than the starting point
yes at x = -2
as for how to do this without areas under the curve, I'm not sure
I think it is just logic in this situation, because there is just so much negative f '
I didn't even calculate the actual area things
Might want to try a mean value. On [-2,0], average decrease is about -2.5, giving an approximate net decrease of -5 on [-2,0] On [0,2], average decrease is about -1.0, giving an approximate net decrease of -2 on [0,2]. Total decrease is now approximately -7 Continue on this way and see if it ever gets higher than where it started. Note: This is the same method proposed by Jim Thompson, just slightly restated.
I guess you could make the observation that much of f ' is under the x axis, so f spends much of its time decreasing. That's more of a qualitative answer than anything
Yeah, that's actually sorta what I did @tkhunny
Well, apparently you did not believe it. Try it with the "area things" and see if you get the same result. It will be a useful exploration.
Also, you are required to state the Absolute Maximum. What we have stated will help you find WHERE the absolute maximum is, but not WHAT it is.