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burhan101Best ResponseYou've already chosen the best response.0
\[\huge y= \frac{ e^{x} }{ 1+e^{x} }, x \epsilon [0,4]\]
 10 months ago

foziaBest ResponseYou've already chosen the best response.0
values maximum, minimum
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
i find the derivative first and then what?
 10 months ago

foziaBest ResponseYou've already chosen the best response.0
first fint derivative that gives the result y'=ex/(1+ex)2 then eqaute it to zero gives ex=0
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
\[\huge y'=\frac{ e^x }{ (1+e^x) }\]
 10 months ago

foziaBest ResponseYou've already chosen the best response.0
take 2nd derivatv now put the value of x =0 in 2nd derivativ if relt is postv then its min otherwise max
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
@fozia wait, you and I got different derivatives
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
@fozia , you have correctly identified the first derivative, but it will never be equal to zero. Therefore, there is no need to take the second derivative. It is sufficient to just analyze the first derivative, realize that it is always positive, and that the original function is always increasing, so it has no extreme values.
 10 months ago

Abhishek619Best ResponseYou've already chosen the best response.0
check if the function is increasing or decreasing?
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
Here's a graph to show you that it is always increasing
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
how do i check if its inc/dec?
 10 months ago

Abhishek619Best ResponseYou've already chosen the best response.0
its first derivative is always a positive, hence it is increasing for all [0.4]. the minimum value will be at x=0, maximu will be at x=4.
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
Read my first post. That will tell you. That numerator of the first derivative is always positive. So is the denominator.
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
No extreme values for domain of all x. min and max though at the endpoints for the given problem domain.
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
That's because "e" is a positive base, so any exponent you put on it will result in a positive number.
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
Do you see that fozia's derivative is correct? That's where you should start.
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
Use the quotient rule to get the derivative. Do you need help with that?
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
@burhan101 I have 2 pending questions posted for you here.
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
@tcarroll010 im trying to figure out how that derivative is right
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
& yes i am using the quotient rule
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
\[\huge \frac{ (1+e^x)(e^x)(e^x)(e^x)}{ (1+e^x)^2 }\]
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
\[\frac{ (1 + e ^{x})e ^{x}  e ^{x}e ^{x} }{ (1 + e ^{x})^{2} } = \frac{ e ^{x} + e ^{2x}  e ^{2x} }{ (1 + e ^{x})^{2} }\]
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
In the numerator, you are left with only e^x and the denominator is the original denominator squared.
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
So, there is no need to take the second derivative. It is sufficient to just analyze the first derivative, realize that it is always positive, and that the original function is always increasing, so it has no extreme values, if your domain is all x. But your domain is limited, so you have your min and max at the xvalue endpoints.
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
but dont i plug in 0 and 4 in f(x) ?
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
So, min at: e^0 / (1 + e^0) max at: e^4 / (1 + e^4)
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
All good now, @burhan101 ?
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
uw! Good luck in all of your studies and thx for the recognition! @burhan101
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
thank you very much, you do explain things very clear !
 10 months ago

tcarroll010Best ResponseYou've already chosen the best response.1
I just like to help. Kind words on your part!
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
For this function \[\huge f(x)= 2\sin4x+3 ; [0, \pi]\] i get the derivative as \[\huge f'(x)=8\cos4x \] To find the extreme values, do i plug in the endpoints into f(x) ? @tcarroll010
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
are u done with this equation
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
dannn:) ! no im not, do i plug the endpoints into the function ?
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
explain the meaning of an extreme value to me
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
an absolute mx or an absolute min
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
so that means the slope there is 0
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
but u must check the end points too incase its just a local max or local min there
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
okay lemme give u some simpler exmaples
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
what are the extreme values for a parabola
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
okay and the slope there is?
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
so that means the derivative there is?
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
dw:1371749935529:dw
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
0/8 = 0dw:1371749995868:dw
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
@bahrom7893 http://multiplayerchess.com/#!/5gqIqmm
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
hello bahrom jhanny wants us to play a game
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
what's the next step ..
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
1what values of x wud make cos4x=0 think about cos pi/2=0 so what much it be
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
ill give u one of the values that is in between 0 and pi cos(4(pi/8)) = 0 thats one
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
would i keep my calculator in degrees or radians?
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
heyy dont be silly u shud know this stuff!! we been doing trig of a while remember where cosx graph = 0
 10 months ago

burhan101Best ResponseYou've already chosen the best response.0
dw:1371751462417:dw
 10 months ago

Loser66Best ResponseYou've already chosen the best response.0
@dan815 I don't know why everybody here ignores the ends of interval when they find out the max, min. My prof always asked us to consider those points, too.
 10 months ago

dan815Best ResponseYou've already chosen the best response.1
i told him to look at those points too :) but its not really needed in this case
 10 months ago
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