Question

i just can't understand the use of dy/dx... (differentiation) why is it use to solve equation...??

Answer 1

do you have an example?

Answer 2

\[dx=\Delta x= x_2-x_1\]
just an easier way to write the "difference of"

Answer 3

this is one of the question example...

"An industrial shed is to have total floor space of 600m^2 and is to be divided into 3 rectangular rooms of equal size. the wall, internal and external will cost $60 per meter to build. what dimensions should the shed have to minimize the cost of the walls"...
we have done this question in class by finding the equation that can be form... but then there were some solution using 1st dy/dx n 2nd dy/dx... ?? =.=" .. why??

these dy/dx really haunt me...

Answer 4

m=dy/dx
m=slope
does that help?

Answer 5

equation gain : 3XY=600 --------------(1)

(total length)L=6X+4Y-----------(2)

then i insert eq (1) into (2) and get
L=6x+(800/X)

total cost
C(X)=\[60(6X+\frac{ 800 }{ X })\]

\[\frac{ dc }{ dx }\] \[= 360-\frac{ 48000 }{ X^{2} }\]

\[\frac{ dc }{ dx }=0\]

therefore

\[360-\frac{ 48000 }{ x ^{2} }=0\]
x= 11.547 m

from equation y
we will get y=17.321 m

and then i use

\[C''=\frac{ 96000 }{ x ^{3} }\]

x=11.54
\[\frac{ 96000 }{ 11.547^{3} }=62.31\]
\[62.31>0\]
therefore its minimize cost....

the thing is... starting from total cost till the end i don't understant a thing why i'm using the dy/dx... if u know some good site instead the wiki... explaining about the dy/dx ... might be help full ... =)

Answer 6

dy/dx is finding the derivative of equation y with respect to x

it also happens to be the slope of any given point x on the graph y

why you are using it, the derivative of an equation gives you an equation that gives you the slope of an equation for any point x that you input, this is especially useful because maximum and minimums of graphs usually have slopes of 0

so by finding the derivative of an equation then setting it equal to 0, one is able to easily determine the coordinate of the max/min

Answer 7

i understand it now... but why am i using derivative at the cost C(X)=60L equation only? how can this C(x)=60L form a graph??

Answer 8

pretend C(x)= y
or f(x)=y
this is assuming these are equations in terms of x

Answer 9

so its mean the X=11.547 m that i've got is maybe the max or the min point...
is what i'm try to digest here is right??

so what is actually the difference of 1st derivative and 2nd derivative...??

Answer 10

1st derivative is useful because the zeros(roots) are max and min points
2nd derivative is the derivative of the 1st derivative

ex.
\[y=x^2\]
\[y'=2x\]
\[y''=2\]

derivatives are denoted by the little apostraphe and please ignore my spelling

Answer 11

2nd derivative zeros can be used for a test, but i dont remember the exact function of them

Answer 12

aa... i've know that the y'' is to fine concavity.. but i'm not really sure what is it about... but something to do about... the increasing or decreasing of something. ahaha... *i don't mind about the spelling ^.^ coz i think i also make mistakes on my spelling too.. thank you very much.. its really help full.. it's my first time using this site... it's really interesting n helpful ... =)