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Whoa, whoa, what?

I'm in Calculus as well, and.. you must be farther than me. Because we never learned maxes and mins. You don't by chance mean the limits as x approaches positive and negative infiniti, do you?

Past that. Have you done derivatives yet?
Apparently this is a step or two before finding the area under a curve and that kind of fun stuff. xp


My current problem is figuring out how to find the maxes and mins of a derivative of a function within a certain range. We were given:

If f(c) is a max or min, then f'(c) = 0 or f'(c) is undefined. The converse is not true. Counter example would be a ledge.
Critical Points -> let f be defined at c.
If f'(c) = 0 or f'(c) is undefined, then c is a critical number of f.
Extrema -> let f be defined on an interval (I) containing c
1.) f(c) is the absolute max of f provided f(c) > f(x) for all x's in I
2.) f(c) is the absolute min of f provided f(c) < f(x) for all x's in I
In order to find extremas we must find the critical points then test the critical and end points.

Can someone explain this to me in plain english? I just don't get it. How can there be a max and min for a line? or for a curve with multiple fluxuations, like a sine curve? I am so cunfuzzled

Oh gosh. I wish I wasn't in stupid math anymore. D: So sad that I dropped from math honors level.


Those look like smileys.

We recently went over that in my calculus class, so I can help ya out, but give me some time to get it together first. I'll post again when I get it.

First of all, I tend to explain things in such a way that people... don't usually follow well sweatdrop , so if I'm terribly confusing, just let me know and I'll try to explain differently. Second, the following information is specifically for curves within a limited domain. When they talk about have maximums and minimums they are talking about in a small area unless they talk about absolute or global ones. Absolute or global means that those are the max or min values for the WHOLE graph within your domain. Relative maxes and mins occur within a smaller area of the curve inside your domain, a matter of one point being higher or lower than the two points on either side. For example, on a sine curve, EACH time the curve gets to its highest point, that is the relative max for that area and it goes the same way for mins. Also, if you have a curve that goes up to y=3, back down somewhere, and then back up to y=5, both 3 AND 5 are relative maxes; 5 would be the absolute max here.


That is saying that whenever you have a max or min in the function, the value of the derivative of the function at that point will be 0 or undefined exclaim but NOT indeterminate exclaim In case you don't know, undefined is when a rational is some number over 0, like 4/0. Indeterminate is when a rational is 0/0. The converse part is saying that just because f'(c)=0 or is undefined it does not mean that you have a max or min there, so you have to test the points that you find.

I think this post is long enough for now... Let me know if you need more help or if any of this confuses you more or whatever.

Actually, you explained what I needed to hear. I already knew the max and min stuff, just not why I needed to test them.

Thank you both.