Hey, Amistre64, can you help me with a derivative, please?

- anonymous

Hey, Amistre64, can you help me with a derivative, please?

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- amistre64

maybe..whatcha got?

- anonymous

\[f(x)=e ^{x }-11e ^{-x}-12x\]

- 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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## More answers

- anonymous

Are you there ?

- amistre64

imhere

- amistre64

the derivative of e^x = e^x
teh derivative of -11e^-x = +e^-x
derivative of -12x = 12

- amistre64

e = oilers number = 2.71828182845905...

- anonymous

But doesn't that e have a funny latin name or something?

- anonymous

How about the second derivative?

- amistre64

its named ofter euler, pronounced oiler

- anonymous

oh, duh! ; )

- 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

\[f(x) = e^x -11e^{-x}-12x\]
\[f'(x) = e^x + 11e^{-x} -12\]
\[f''(x) = e^x -11e^{-x}\]

- 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

e is a regular number; it just has a special name :)

- amistre64

but yes, find them the regular way

- 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

http://www.wolframalpha.com/input/?i=e^x+-11e^%28-x%29-12x

- amistre64

you can approximate it with 2.7183

- 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

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

ln(x) -11/ln(x) - 12x maybe?

- amistre64

ln(x) = e
and 1/ln(x) = e^(-x)

- amistre64

well, ln(y) is a better term than x in that case but thats semantics

- 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

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

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

e^x^2 -12e^x +11= 0 is a quadratic

- amistre64

do you know what inflection and min and max are?

- amistre64

a^2 -12a + 11 = 0 when....
(a-11)(a-1) = a = 1 and a = 11

- 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

when e^x = 1 or 11 we should test this

- 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

and an 84% is a B so :)

- 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

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

uh...I guess. Exponents aren't my strong point. None of it really, it's been way too long to just remember!

- amistre64

normally a negative exponent means to invert it; let me recheck that thought tho

- anonymous

I doknow that x^-3, say, is 1/x^3

- amistre64

spose we saw a normal number like 2^x; how would it graph look?

- anonymous

I don't know.

- amistre64

if we plot it it looks like this...

##### 1 Attachment

- amistre64

if we plot 2^(-x) it loks like this, the one in red

##### 1 Attachment

- anonymous

dont' mean to be rude, but there wasn't a line in red in that second attachment.

- amistre64

which is the same graph as (1/2)^x lol.... forgot to save before i attached

##### 1 Attachment

- amistre64

##### 1 Attachment

- amistre64

http://www.wolframalpha.com/input/?i=%281%2F2%29^x

- 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

soo... 2^-x is the same as (1/2)^x

- amistre64

the last jpg has both lines

- 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

got that graph. It is symmetrical about the y axis. That's about all I know.

- 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

\[e^x +\frac{11}{e^x}-12=0\]

- amistre64

lets see :)

- amistre64

\[e^x +\frac{11}{e^x} = 12\] right?

- anonymous

yes, tht is algebra! i like algebra! alot!

- amistre64

\[\frac{(e^x)^2 + 11}{e^x} = 12\]

- amistre64

\[(e^x)^2 + 11 = 12e^x\]

- amistre64

\[(e^x)^2 -12(e^x) + 11 = 0\]

- amistre64

u = e^x
\[u^2 -12u +11 = 0\]

- amistre64

solve for u

- anonymous

don't mean to sound obtuse, but this is the derivative you are solving for 0, right?

- amistre64

yes :)

- anonymous

ok that factors to u-11 and u-1, which give u=11 and u=1. Are those critical points, then?

- amistre64

are we looking to solve an equation with u? or e^x?

- anonymous

The e one. I need to find critical points so I can find the inflection points and the extrema.

- amistre64

u = 11, or 1
u = e^x
e^x = 11, or 1

- amistre64

e^x = 11 ; ln(11) = x
e^x = 1 ; ln(1) = x
now this is calculator time....

- amistre64

ln(11) = 2.398....
ln(1) = 0 are our critical points

- anonymous

Does this problem have a domain of negative to positive infinity?

- amistre64

teh tree terms all have domains that are form -inf to inf

- amistre64

so yes

- 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

http://www.wolframalpha.com/input/?i=%28e^x%29-%2811%2F%28e^x%29%29-12x tells me im right :)

- 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

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

my kids call me 'daddy' :)

- anonymous

aw, how many?

- amistre64

2... 13 and 15

- 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

:) thnx. Lotta kids on your end, nothing better to do in the winter? ;)

- 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

its been chillly these past few days, had a front move thru and cooled us down

- anonymous

Cooled you down to what? 83 instead of 85? lol

- amistre64

lotta kids is is a sign of catholic or mormon... statistically speaking that is

- amistre64

:) water freezes at 60 here

- anonymous

my husband is a reformed catholic. We are both lutheran now. But they don't believe in birth control either. Ha!

- amistre64

I grew up with German Catholic family; joined the Mormons with mom back in 84 tho and aint looked back since :)

- 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

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

lived in north carolina for a few months after mom died... that was nice country

- amistre64

the exact form would be ln(11) and 0 for our critical points

- 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

\[f''(x)=e^x -\frac{11}{e^x}\]

- 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

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

you teach at college?

- amistre64

\[\frac{(e^x)^2 -11}{e^x} = 0\]

- amistre64

i gotta get a masters in math to teach at collegge, so thats what Im working on now

- anonymous

That is so awesome. What kind of math do you want to teach? Me, I want to teach algebra.

- amistre64

u = e^x is still a good substitute; so lets do this:
u^2 - 11 = 0 when u = ?

- 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

I tried ti get a tutring job at the college here, but they dont seem to want my abilities...

- 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

my guess is abt 1.199...

- amistre64

florida to illinios is a long commute lol

- anonymous

what is 1.199?

- 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

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

Bradenton is about 1.5hours to the south of me..

- 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

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

I taught myself it really; and the stuff I aint to sure about, I pick up on in class

- amistre64

download firefox; this site is much better with firefox

- anonymous

I have firefox and use it for most of the stuff, but some websites don't support it, like MathXL for instance.

- 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

then I got me some calculus books from the library and taught myself up to like cal3 or 4

- anonymous

I got hung up on a story problem in my 15yr old daughter's algebra book last night. Bery frustrating!!!

- anonymous

I mean very, not bery.

- amistre64

:) i read a book called, "How to solve word problems" that was very informative.

- 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

I can't figure out how they have t and call it speed.

- amistre64

had to look at an email; trying to get into a 4year college for the fall instead of community college

- 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

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

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

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

yeah, gotta show resoect to someone who can hold down the fort like that these days

- 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

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

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

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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