Thread: Need little help listing from smallest to largest

Hey,
I need little help with this problem:


Can someone please show me how to find the smallest one (or just anyone for that matter?) I'm not looking for the final answer, just show me to find any of them and I'll take it from there. I do have an example in the book similar to this one, but it only gives the final answer, which is not what I'm looking for.

First, can you see that c) is negative and d) is positive?

Originally Posted by MarkFL2

First, can you see that c) is negative and d) is positive?

I can't, mainly because I'm not sure how to plug 2 and 1 for c) or 1 and -1 for d)

You don't need to, nor can you, plug in these values since you are not told what actually is. You are being expected to observe that the area between the function and the x-axis represents the magnitude of the definite integral, which is positive where and negative when .

So, which one would you say is the largest in value out of all the choices and why?

Originally Posted by MarkFL2

You don't need to, nor can you, plug in these values since you are not told what actually is. You are being expected to observe that the area between the function and the x-axis represents the magnitude of the definite integral, which is positive where and negative when .

So, which one would you say is the largest in value out of all the choices and why?

This is starting to make sense. I'd say e) is the largest, given it combines the area for d) and b) (although b) is negative, it turns positive because of the absolute value.)

Yes, that's absolutely correct! Now, which would you say is the smallest and why?

Originally Posted by MarkFL2

Yes, that's absolutely correct! Now, which would you say is the smallest and why?

I'd say b) is the smallest, given its the only negative out of them all.

Originally Posted by theunforgiven

I'd say be is the smallest, given its the only negative out of them all.

It's not the only negative, but it takes up the most area below the x axis. So yes, it's the smallest...

Originally Posted by Prove It

It's not the only negative, but it takes up the most area below the x axis. So yes, it's the smallest...

Oh my bad. C) is negative as well.

So, the final answer would be b<c<f<a<d<e

Looks good to me

How about f)? What would you say its value is?

So, given what you have so far, can you now give them in the required order?

edit: I was too slow.

Originally Posted by MarkFL2

How about f)? What would you say its value is?

So, given what you have so far, can you now give them in the required order?

edit: I was too slow.

Haha. f) would be 0. It's just a point on the graph.

f) is asking for the derivative, so you need to look at the slope of the curve at that point, which does incidentally look like it is zero.

Originally Posted by MarkFL2

f) is asking for the derivative, so you need to look at the slope of the curve at that point, which does incidentally look like it is zero.

Oh I see. Guess I just got lucky with that one lol.