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burhan101
 2 years ago
Determine the extreme values:
burhan101
 2 years ago
Determine the extreme values:

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burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0\[\huge y= \frac{ e^{x} }{ 1+e^{x} }, x \epsilon [0,4]\]

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0i find the derivative first and then what?

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

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0\[\huge y'=\frac{ e^x }{ (1+e^x) }\]

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

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0@fozia wait, you and I got different derivatives

tcarroll010
 2 years ago
Best 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.

Abhishek619
 2 years ago
Best ResponseYou've already chosen the best response.0check if the function is increasing or decreasing?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Here's a graph to show you that it is always increasing

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0how do i check if its inc/dec?

Abhishek619
 2 years ago
Best ResponseYou've already chosen the best response.0its 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.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Read my first post. That will tell you. That numerator of the first derivative is always positive. So is the denominator.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1No extreme values for domain of all x. min and max though at the endpoints for the given problem domain.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1That's because "e" is a positive base, so any exponent you put on it will result in a positive number.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Do you see that fozia's derivative is correct? That's where you should start.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1Use the quotient rule to get the derivative. Do you need help with that?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1@burhan101 I have 2 pending questions posted for you here.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0@tcarroll010 im trying to figure out how that derivative is right

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0& yes i am using the quotient rule

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0\[\huge \frac{ (1+e^x)(e^x)(e^x)(e^x)}{ (1+e^x)^2 }\]

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ (1 + e ^{x})e ^{x}  e ^{x}e ^{x} }{ (1 + e ^{x})^{2} } = \frac{ e ^{x} + e ^{2x}  e ^{2x} }{ (1 + e ^{x})^{2} }\]

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1In the numerator, you are left with only e^x and the denominator is the original denominator squared.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1So, 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.

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0but dont i plug in 0 and 4 in f(x) ?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1So, min at: e^0 / (1 + e^0) max at: e^4 / (1 + e^4)

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1All good now, @burhan101 ?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1uw! Good luck in all of your studies and thx for the recognition! @burhan101

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0thank you very much, you do explain things very clear !

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.1I just like to help. Kind words on your part!

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0For 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

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1are u done with this equation

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0dannn:) ! no im not, do i plug the endpoints into the function ?

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1explain the meaning of an extreme value to me

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0an absolute mx or an absolute min

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1so that means the slope there is 0

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1but u must check the end points too incase its just a local max or local min there

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1okay lemme give u some simpler exmaples

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1what are the extreme values for a parabola

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1okay and the slope there is?

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1so that means the derivative there is?

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1371749935529:dw

dan815
 2 years ago
Best ResponseYou've already chosen the best response.10/8 = 0dw:1371749995868:dw

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1@bahrom7893 http://multiplayerchess.com/#!/5gqIqmm

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1hello bahrom jhanny wants us to play a game

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0what's the next step ..

dan815
 2 years ago
Best ResponseYou've already chosen the best response.11what values of x wud make cos4x=0 think about cos pi/2=0 so what much it be

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1ill give u one of the values that is in between 0 and pi cos(4(pi/8)) = 0 thats one

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0would i keep my calculator in degrees or radians?

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1heyy dont be silly u shud know this stuff!! we been doing trig of a while remember where cosx graph = 0

burhan101
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1371751462417:dw

Loser66
 2 years ago
Best 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.

dan815
 2 years ago
Best ResponseYou've already chosen the best response.1i told him to look at those points too :) but its not really needed in this case
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