Steps to solve a max /min problem (Differentiation) (1 Viewer)

[atar90plus]

Hello
I am wondering if anyone can tell me what are the steps / procedures in solving any maximum and minimum problems.

Thanks

 

[deswa1]

This is off the top of my head, so I've probably missed some steps. If you give a quick problem, I can solve it and then list the steps if I missed stuff:

1. Write out all the information. For example, if its a cylinder minimisation problem, write the equation for the volume of a cylinder etc.
2. Use the information to express one variable in terms of another. For example, if you know that one side of a rectange is twice the other, then if the side lengths are x and y, y=2x
3. Sub in this information into the equation you wrote down first off (in this case the area of a rectangle)
4. Differentiate and solve for 0 to find stationary points
5. Test nature of stationary points
6. Answer the question. For example, the question might ask for the minimum area or minimum side length etc. Use the information you just worked out to answer it.

 

[asari]

Hi can you please solve this :
Find the dimensions of the cylindrical can of greatest volume that can be made from <a href="http://www.codecogs.com/eqnedit.php?latex=\large \inline \fn_phv 600\pi cm^{2}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\large \inline \fn_phv 600\pi cm^{2}" title="\large \inline \fn_phv of sheet metal

 

[nightweaver066]

Hi can you please solve this :
Find the dimensions of the cylindrical can of greatest volume that can be made from <a href="http://www.codecogs.com/eqnedit.php?latex=\large \inline \fn_phv 600\pi cm^{2}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\large \inline \fn_phv 600\pi cm^{2}" title="\large \inline \fn_phv of sheet metal

Should make your own thread and not bump something posted a long time ago lol.

Use surface area formula, i.e.

Write volume formula, i.e.

Use these two formulas to get something in terms of V and h or V and r and you can do the rest.

 

[asari]

Should make your own thread and not bump something posted a long time ago lol.

Use surface area formula, i.e.

Write volume formula, i.e.

Use these two formulas to get something in terms of V and h or V and r and you can do the rest.

I've got 10cm and 25cm for some reason

 

[asari]

ah, dw, I found my mistake thanks

 

[qwerty44]

This is off the top of my head, so I've probably missed some steps. If you give a quick problem, I can solve it and then list the steps if I missed stuff:

1. Write out all the information. For example, if its a cylinder minimisation problem, write the equation for the volume of a cylinder etc.
2. Use the information to express one variable in terms of another. For example, if you know that one side of a rectange is twice the other, then if the side lengths are x and y, y=2x
3. Sub in this information into the equation you wrote down first off (in this case the area of a rectangle)
4. Differentiate and solve for 0 to find stationary points
5. Test nature of stationary points
6. Answer the question. For example, the question might ask for the minimum area or minimum side length etc. Use the information you just worked out to answer it.

Not much more complicated than this^