anonymous
  • anonymous
Hey, Amistre64, can you help me with a derivative, please?
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
maybe..whatcha got?
anonymous
  • anonymous
\[f(x)=e ^{x }-11e ^{-x}-12x\]
anonymous
  • anonymous
I need to find the local extreme points and the inflection points, which means I need the first and second derivatives. I do not know what to do with that e. It's not a regular e it's that math e. What's it called in math language?

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anonymous
  • anonymous
Are you there ?
amistre64
  • amistre64
imhere
amistre64
  • amistre64
the derivative of e^x = e^x teh derivative of -11e^-x = +e^-x derivative of -12x = 12
amistre64
  • amistre64
e = oilers number = 2.71828182845905...
anonymous
  • anonymous
But doesn't that e have a funny latin name or something?
anonymous
  • anonymous
How about the second derivative?
amistre64
  • amistre64
its named ofter euler, pronounced oiler
anonymous
  • anonymous
oh, duh! ; )
amistre64
  • amistre64
the second derivative is similar except for -12 goes to 0 e^x goes to e^x again and +11e^-x for to -11e^-x
amistre64
  • amistre64
\[f(x) = e^x -11e^{-x}-12x\] \[f'(x) = e^x + 11e^{-x} -12\] \[f''(x) = e^x -11e^{-x}\]
anonymous
  • anonymous
So do I find the points of inflection and the extrema the way I would as if they were regular numbers? I just don't know what to do with something that isn't a regular number, like this and delta and pi. They really bother me. I don't mind the x's in algebra, but these are way out there.
amistre64
  • amistre64
e is a regular number; it just has a special name :)
amistre64
  • amistre64
but yes, find them the regular way
anonymous
  • anonymous
ok, so if I am finding the points of interest using e, do I use the number value for it or do I just leave it as e?
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=e^x+-11e^%28-x%29-12x
amistre64
  • amistre64
you can approximate it with 2.7183
anonymous
  • anonymous
would I do that normally with a problem that has e in it? Use the number value, I mean. Is that the way it's supposed to be done? Does that link show stuff about e?
amistre64
  • amistre64
e is an exact value, so any number form of it is going to be an approximation; then way we solve for this is prolly thru logarithms
amistre64
  • amistre64
ln(x) -11/ln(x) - 12x maybe?
amistre64
  • amistre64
ln(x) = e and 1/ln(x) = e^(-x)
amistre64
  • amistre64
well, ln(y) is a better term than x in that case but thats semantics
anonymous
  • anonymous
This is making my stomach upset, all this crazy math stuff with these weird alien symbols. It's really scary how much I don't know and to think I am getting an A in calculus! Don't ask me how!
amistre64
  • amistre64
f′(x)= e^x +11e^(−x) −12 = 0 when e^x +11e^(−x) = 12 i dont think theres an easy way to desribe it
anonymous
  • anonymous
I took a calculus test today and this was on it, finding the extrema and points of inflection, and I just never saw such a problem. It wasn't in our homework problems, and since i am taking this online it's not like I can go ask the instructor. I just don't know what to do with it.
amistre64
  • amistre64
e^x^2 -12e^x +11= 0 is a quadratic
amistre64
  • amistre64
do you know what inflection and min and max are?
amistre64
  • amistre64
a^2 -12a + 11 = 0 when.... (a-11)(a-1) = a = 1 and a = 11
anonymous
  • anonymous
We just got done with the chapters and I did really well with the trig functions and the regualr numbers in finding the critical points and local max and min and extreme max and min, but this one i didn't work before and i don't have the common sense to be able to apply the regular rules to something like this. If someone doesn't show me step by step, I will not understand. Got a 12.7 out of 15 points on the test.
amistre64
  • amistre64
when e^x = 1 or 11 we should test this
amistre64
  • amistre64
that doesnt seem to work out... more than likely it just a matter of using what you know to figure out what you dont think you know
amistre64
  • amistre64
and an 84% is a B so :)
anonymous
  • anonymous
But what if you don't know anything? What then? That's the way I feel about calculus most of the time! I work on Math XL sometimes 14 hours a day, and only got a B. My overall greade is a 96% but I can feel it slowly slipping away... How do I find out how to solve that e problem for the critical points and stuff? Any suggestions?
amistre64
  • amistre64
first derive it; and see what you can do to it algebraicly f'(x) = e^x +11e^(−x) −12 ; we know that a negative exponent is a reciprocal right?
anonymous
  • anonymous
uh...I guess. Exponents aren't my strong point. None of it really, it's been way too long to just remember!
amistre64
  • amistre64
normally a negative exponent means to invert it; let me recheck that thought tho
anonymous
  • anonymous
I doknow that x^-3, say, is 1/x^3
amistre64
  • amistre64
spose we saw a normal number like 2^x; how would it graph look?
anonymous
  • anonymous
I don't know.
amistre64
  • amistre64
if we plot it it looks like this...
1 Attachment
amistre64
  • amistre64
if we plot 2^(-x) it loks like this, the one in red
1 Attachment
anonymous
  • anonymous
dont' mean to be rude, but there wasn't a line in red in that second attachment.
amistre64
  • amistre64
which is the same graph as (1/2)^x lol.... forgot to save before i attached
1 Attachment
amistre64
  • amistre64
1 Attachment
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=%281%2F2%29^x
anonymous
  • anonymous
no red line there either. I'm sorry to be such a pain. Just when I think I may actually be not so dumb, I realize I was mistaken. I know nothing about any of this and i really don't know what to do!
amistre64
  • amistre64
soo... 2^-x is the same as (1/2)^x
amistre64
  • amistre64
the last jpg has both lines
amistre64
  • amistre64
e^-x = (1/e)^x ; its just a number like 2 or 5 just written in a way we can express it exactly
anonymous
  • anonymous
got that graph. It is symmetrical about the y axis. That's about all I know.
anonymous
  • anonymous
So i might be able to do that e problem with using the value for it? Do I still need logs for that?
amistre64
  • amistre64
\[e^x +\frac{11}{e^x}-12=0\]
amistre64
  • amistre64
lets see :)
amistre64
  • amistre64
\[e^x +\frac{11}{e^x} = 12\] right?
anonymous
  • anonymous
yes, tht is algebra! i like algebra! alot!
amistre64
  • amistre64
\[\frac{(e^x)^2 + 11}{e^x} = 12\]
amistre64
  • amistre64
\[(e^x)^2 + 11 = 12e^x\]
amistre64
  • amistre64
\[(e^x)^2 -12(e^x) + 11 = 0\]
amistre64
  • amistre64
u = e^x \[u^2 -12u +11 = 0\]
amistre64
  • amistre64
solve for u
anonymous
  • anonymous
don't mean to sound obtuse, but this is the derivative you are solving for 0, right?
amistre64
  • amistre64
yes :)
anonymous
  • anonymous
ok that factors to u-11 and u-1, which give u=11 and u=1. Are those critical points, then?
amistre64
  • amistre64
are we looking to solve an equation with u? or e^x?
anonymous
  • anonymous
The e one. I need to find critical points so I can find the inflection points and the extrema.
amistre64
  • amistre64
u = 11, or 1 u = e^x e^x = 11, or 1
amistre64
  • amistre64
e^x = 11 ; ln(11) = x e^x = 1 ; ln(1) = x now this is calculator time....
amistre64
  • amistre64
ln(11) = 2.398.... ln(1) = 0 are our critical points
anonymous
  • anonymous
Does this problem have a domain of negative to positive infinity?
amistre64
  • amistre64
teh tree terms all have domains that are form -inf to inf
amistre64
  • amistre64
so yes
amistre64
  • amistre64
the inflection point is the axis of symettry of the quadratic... so at x = halfway between 0 and 2.398.... is your inflection point
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=%28e^x%29-%2811%2F%28e^x%29%29-12x tells me im right :)
amistre64
  • amistre64
the main point here is that you see how I turned this into a quadratic, something that you shuold be familiar with alrady
anonymous
  • anonymous
But do I have to have exact numbers? I mean the way we have been doing this, every point of inflection and max and min all have very specific cooridnates. I'm sorry I' m so dumb at this. I'll bet you're a male, right? Pardon me, but I cannot tell for sure by your user name and I personally think men are much better with numbers. All my math teachers were male, all though my years of school.
amistre64
  • amistre64
my kids call me 'daddy' :)
anonymous
  • anonymous
aw, how many?
amistre64
  • amistre64
2... 13 and 15
anonymous
  • anonymous
I have a 13 and 15 year old too! I atually have 5, 6,8,11,13,15. 4 girls and a boy. Your kids are so lucky to have such a smart dad!
amistre64
  • amistre64
:) thnx. Lotta kids on your end, nothing better to do in the winter? ;)
anonymous
  • anonymous
lol~!!!!!!!!!!!! funny guy! Never wanted kids, actually, but now...they are somethin aren't they? Actually, they will be home in a couple of minutes. Almost summer now, I bet it's HOT there already!
amistre64
  • amistre64
its been chillly these past few days, had a front move thru and cooled us down
anonymous
  • anonymous
Cooled you down to what? 83 instead of 85? lol
amistre64
  • amistre64
lotta kids is is a sign of catholic or mormon... statistically speaking that is
amistre64
  • amistre64
:) water freezes at 60 here
anonymous
  • anonymous
my husband is a reformed catholic. We are both lutheran now. But they don't believe in birth control either. Ha!
amistre64
  • amistre64
I grew up with German Catholic family; joined the Mormons with mom back in 84 tho and aint looked back since :)
anonymous
  • anonymous
not familiar with the mormon religion. Just took a christian worldview course before this calculus. It was awesome! I know quite a few people in Florida. do you like florida?
amistre64
  • amistre64
florida is ok..... been here for about 40 years now; borned in Lakeland and lived in dadecity area most me life.... thats north of tampa
amistre64
  • amistre64
lived in north carolina for a few months after mom died... that was nice country
amistre64
  • amistre64
the exact form would be ln(11) and 0 for our critical points
anonymous
  • anonymous
ok and badk to math...sorry. I am definitely female; nosy and all! Ssorry! But how do you know all this math stuff? Were you a teacher ever? Or do you just like numbers?
amistre64
  • amistre64
\[f''(x)=e^x -\frac{11}{e^x}\]
amistre64
  • amistre64
ive always liked math; but grew up doing labor and was a carpenter for 15 years, hurt my back and decided to get a degree in Math to teach at college
anonymous
  • anonymous
That ln(ll) thing actually looks familiar. I need to go back and look at the homework problems. IE is really bad on this website! I'ts jmping all over the place!
anonymous
  • anonymous
you teach at college?
amistre64
  • amistre64
\[\frac{(e^x)^2 -11}{e^x} = 0\]
amistre64
  • amistre64
i gotta get a masters in math to teach at collegge, so thats what Im working on now
anonymous
  • anonymous
That is so awesome. What kind of math do you want to teach? Me, I want to teach algebra.
amistre64
  • amistre64
u = e^x is still a good substitute; so lets do this: u^2 - 11 = 0 when u = ?
amistre64
  • amistre64
Any college math I would like to teach, I see the way the older folks light up when the finally realize something that they really knew all along
amistre64
  • amistre64
I tried ti get a tutring job at the college here, but they dont seem to want my abilities...
anonymous
  • anonymous
This is really crazy, me asking you this extremely complicated question online. I need a tutor! But I don't think you'd drive from Florida to Illinois to tutor, so...what to do? I think now that I have the derivative of that, maybe I will try to do something with it. Now that I took the tesst, it doesn't matter so mucch unless I retake it and can get that one correct this time.
amistre64
  • amistre64
my guess is abt 1.199...
amistre64
  • amistre64
florida to illinios is a long commute lol
anonymous
  • anonymous
what is 1.199?
anonymous
  • anonymous
My best friend moved to florida about 7 years ago, and I miss her so much. She lives in Bradenton, the home to Tenth Avenue North.
amistre64
  • amistre64
ok... i took the 2nd derivative to be (e^x)^2 - 11 = 0 to find the inflection points... whichi i believe are just halfway between 0 and ln(11); so thats my prediction till I see otherwise :)
amistre64
  • amistre64
Bradenton is about 1.5hours to the south of me..
anonymous
  • anonymous
how do you know all this math stuff? I spent literally 80 hours in the past 5 days doing this and I still don't know it!
amistre64
  • amistre64
e^x = sqrt(11) or e^x = -sqrt(11). -sqrt(11) is not possible so that leaves e^x = sqrt(11) ln(sqrt(11))= x = 1.199.... I was right lol
amistre64
  • amistre64
I taught myself it really; and the stuff I aint to sure about, I pick up on in class
amistre64
  • amistre64
download firefox; this site is much better with firefox
anonymous
  • anonymous
I have firefox and use it for most of the stuff, but some websites don't support it, like MathXL for instance.
amistre64
  • amistre64
First week in intermediate algeabra and I was done with all the homework assignments; so my teacher gave me the college algebra/trig book and I finished that one too
amistre64
  • amistre64
then I got me some calculus books from the library and taught myself up to like cal3 or 4
anonymous
  • anonymous
I got hung up on a story problem in my 15yr old daughter's algebra book last night. Bery frustrating!!!
anonymous
  • anonymous
I mean very, not bery.
amistre64
  • amistre64
:) i read a book called, "How to solve word problems" that was very informative.
anonymous
  • anonymous
There's really a book that tells you how to solve word problems? The ones I get the most hung up on are the d=rt ones.
anonymous
  • anonymous
I can't figure out how they have t and call it speed.
amistre64
  • amistre64
had to look at an email; trying to get into a 4year college for the fall instead of community college
amistre64
  • amistre64
and pell grant refund came in so I can have some money to vist the kids this weekend :) YAY!!! been like 3 weeks without them :)
anonymous
  • anonymous
Couldn't imagine not seeing my kids; it must be hard. I got pell grant money for GCU. It's not so bad in some circumstances being near poverty level! lol ;)
amistre64
  • amistre64
i had to get insurance and car stuff this year and that ate alot of the last stuff..... been riding on empty for a few weeks now just hoping :)
anonymous
  • anonymous
story of my life...riding on empty! I don't work in the real sense of the word and all the burden then falls on my husband which is a huge burden with 5 kids!
amistre64
  • amistre64
yeah, gotta show resoect to someone who can hold down the fort like that these days
anonymous
  • anonymous
yeah, really,. He's really good about it too, just doing it and not complaining about it. Of course, he, on the other hand hasn't done a load of laundry for 16 years or the dishes for even longer! so I guess it all evens out...I clean up after everyone here and he goes out to work so he doesn't have to!
amistre64
  • amistre64
if your happy with the way things have worked out; then thats all the really matters in my opinion. My wife was never happy with things, and ended up simply leaving one day to go play with drugs and ruin her life
amistre64
  • amistre64
i gotta go do some homework assignments for statitstics class. But I got a secret :) The book in the reference section at the library is teh teachers edition so all the answers are in it lol
anonymous
  • anonymous
That's too bad about your wife. Things sometimes don't go the way we want them to, do they? Do you get all the answers for me from your answer manual! Dontcha wish there was one for life? Or maybe they call it the Bible! Have a great day in florida; talk to you very soon! Thanks again.

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