Question

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

Answer 1

maybe..whatcha got?

Answer 2

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

Answer 3

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?

Answer 4

Are you there ?

Answer 5

imhere

Answer 6

the derivative of e^x = e^x

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

derivative of -12x = 12

Answer 7

e = oilers number = 2.71828182845905...

Answer 8

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

Answer 9

How about the second derivative?

Answer 10

its named ofter euler, pronounced oiler

Answer 11

oh, duh! ; )

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

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

Answer 16

but yes, find them the regular way

Answer 17

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?

Answer 18

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

Answer 19

you can approximate it with 2.7183

Answer 20

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?

Answer 21

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

Answer 22

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

Answer 23

ln(x) = e

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

Answer 24

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

Answer 25

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!

Answer 26

f′(x)= e^x +11e^(−x) −12 = 0 when

e^x +11e^(−x) = 12 i dont think theres an easy way to desribe it

Answer 27

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.

Answer 28

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

Answer 29

do you know what inflection and min and max are?

Answer 30

a^2 -12a + 11 = 0 when....

(a-11)(a-1) = a = 1 and a = 11

Answer 31

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.

Answer 32

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

Answer 33

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

Answer 34

and an 84% is a B so :)

Answer 35

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?

Answer 36

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?

Answer 37

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

Answer 38

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

Answer 39

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

Answer 40

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

Answer 41

I don't know.

Answer 42

if we plot it it looks like this...

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

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!

Answer 48

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

Answer 49

the last jpg has both lines

Answer 50

e^-x = (1/e)^x ; its just a number like 2 or 5 just written in a way we can express it exactly

Answer 51

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

Answer 52

So i might be able to do that e problem with using the value for it? Do I still need logs for that?

Answer 53

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

Answer 54

lets see :)

Answer 55

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

Answer 56

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

Answer 57

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

Answer 58

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

Answer 59

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

Answer 60

u = e^x

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

Answer 61

solve for u

Answer 62

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

Answer 63

yes :)

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

u = 11, or 1

u = e^x

e^x = 11, or 1

Answer 68

e^x = 11 ; ln(11) = x

e^x = 1 ; ln(1) = x

now this is calculator time....

Answer 69

ln(11) = 2.398....

ln(1) = 0 are our critical points

Answer 70

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

Answer 71

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

Answer 72

so yes

Answer 73

the inflection point is the axis of symettry of the quadratic... so at x = halfway between 0 and 2.398.... is your inflection point

Answer 74

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

Answer 75

the main point here is that you see how I turned this into a quadratic, something that you shuold be familiar with alrady

Answer 76

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.

Answer 77

my kids call me 'daddy' :)

Answer 78

aw, how many?

Answer 79

2... 13 and 15

Answer 80

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!

Answer 81

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

Answer 82

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!

Answer 83

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

Answer 84

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

Answer 85

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

Answer 86

:) water freezes at 60 here

Answer 87

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

Answer 88

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

Answer 89

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?

Answer 90

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

Answer 91

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

Answer 92

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

Answer 93

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?

Answer 94

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

Answer 95

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