Max/Min (1 Viewer)

[Tommy_Lamp]

Couldnt find another thread on this

But if your asked to find the Maximum surface area, or the minimum volume etc. how do you do it, im completely stumped.

and also, does the order of velocity, displacement and acceleration go like this:
y = velocity
first der. = displacement
second der. = acceleration

Thanks

 

[mizz_smee]

y = displacement
y' = velocity
y'' = acceleration

as for the others i vagly remember but not really
i think it has something to do with solving them algerbraically

 

[withoutaface]

Most of the time you can find an expression for the area which can be differentiated, you equate the first derivative to zero and you know the rest.

 

[Freedom_Dragon]

Couldnt find another thread on this

But if your asked to find the Maximum surface area, or the minimum volume etc. how do you do it, im completely stumped.

Simple Eg:
A grazier wants to fence off a rectangle paddock next to a river, using 120 m of fencing.
120m=3 sides of fencing. The other side is fenced off using a river.

(i) Find an expression for the length, y, of the paddock in terms of its width, x.

120m=2x+y

Answer:
:. y=120-2x (Expression in terms of y)

(ii) Show that the area, A, of the paddock is given by

A=120x-2x^2 "^" means to the power off

We know that the area of any rectangle is width*length
A=x*y

Substitute y=120-2x in A=x*y

Answer:
A=x(120-2x)
:. A=120x-2x^2

(iii) Hence find the dimention which will make the area of the paddock a maximum.

To determine maximum
second der. <0
Also Note
To determine minimum
second der. >0

Answer:
A=120x-2x^2

dA/dx=120-4x (to find the dimention, dA/dx=0, to find the value for x)
120-4x=0
:. x=30m

Sub x=30m into y=120-2x to find the value for y.
y=120-4(30)
:.y=60 m

To ensure that it is a MAX
dA/dx=120-4x
:. d2A/dx2=-4 x=30,y=60 will yield a MAX area.

(iv) Find the maximum area of the paddock.

Answer:
Simply substitue ur "x" & "y" values into ur Area equation
A=x*y
:. A=1800m^2
OR u can just substitute "x" value into
A=120x-2x^2
A=120(30)-2(30)^2
:.A=1800m^2

and also, does the order of velocity, displacement and acceleration go like this:
y = velocity
first der. = displacement
second der. = acceleration
Thanks

Isnt it supposed to be
y=displacement
first der. =velocity
second der. = acceleration

 

[Tommy_Lamp]

wow thanks, thats really helpful

5 reps for you

and thanks smee and justin

 

[Freedom_Dragon]

Hhahahahaaa

Keeps those reps coming..jks

 

[Xayma]

and also, does the order of velocity, displacement and acceleration go like this:
y = velocity
first der. = displacement
second der. = acceleration

Thanks

If you have trouble remembering it just remember what is each one is:

Displacement is a change in position.
Velocity rate of change of displacement vs time.
Acceleration rate of change of velocity vs time.
Jerk rate of change of acceleration vs time (but you will never need to know that).

 

[Tommy_Lamp]

i should know them anyway from physics but meh

thanks

 

[JamiL]

y = displacement
y' = velocity
y'' = acceleration

as for the others i vagly remember but not really
i think it has something to do with solving them algerbraically

actually they usally use x as displacements x' or v as velocity and x'' or a as accell they dont use y cos it can get confuzin

 

[mizz_smee]

actually they usally use x as displacements x' or v as velocity and x'' or a as accell they dont use y cos it can get confuzin

i know that but he used y
and we got taught to use dots not dashes when using x