Why do these calc problems pwn me so much?

[duragezic]

Wha, we started a new chapter in my HS calc class and it has questions like:
"A rectangular box with a square base and no top has a total area of 120 cm^2, what dimensions would give it maximum volume?"

And that is probably the easiest kind. Most are a lot more involved and I have no clue on how to even do that one.
They all seem pretty easy since it usually involves algebra like substitution and solving, then take the derivative, but I can NEVER think of what to do. Like when the teacher goes over it it all seems so easy but I just don't think that way like I read a problem and have NO idea where to start it from.

 

[GiLtY]

Wait until you get to Infinite series.. Taylor Series pwned me :Q

 

[Spac3d]

lol that isn't real calculus.

 

[GroundZero]

probably because you are a tard
and if you spell owned with a p you will never get variables

 

[MacBaine]

Originally posted by: Spac3d
lol that isn't real calculus.

Seriously dude... just wait...

 

[Gibson486]

This is almost a related rate porblem, but it really is not calc. I take it that you are trying to solve via derivative?

 

[phatj]

Wait until you get to Infinite series.. Taylor Series pwned me

0
Im currently takin AB calculus.. infinite series arent all that hard... Taylor series part of the C topic?

 

[Rkonster]

Originally posted by: phatj

Wait until you get to Infinite series.. Taylor Series pwned me

Im currently takin AB calculus.. infinite series arent all that hard...

Umm, they don't teach Taylor series's and such in Calc AB.

 

[oboeguy]

Don't be afraid of this kind of problem. I used to suck at them and now I'm almost done with a PhD in the stuff. It can be done!

 

[TuxDave]

Originally posted by: oboeguy
Don't be afraid of this kind of problem. I used to suck at them and now I'm almost done with a PhD in the stuff. It can be done!

*bows down to the Ph'D* (me being a mere M.S. student)

 

[phatj]

Originally posted by: Rkonster

Originally posted by: phatj

Wait until you get to Infinite series.. Taylor Series pwned me

Im currently takin AB calculus.. infinite series arent all that hard...

Umm, they don't teach Taylor series's and such in Calc AB.

I never said Taylor series were taught in AB. I said infinite series arent all that hard, and infinite series are taught in AB

 

[jmcoreymv]

Just had a test on taylor series in my calc bc class. Wasnt too bad once you go over the material enough times.

 

[RaynorWolfcastle]

Originally posted by: jmcoreymv
Just had a test on taylor series in my calc bc class. Wasnt too bad once you go over the material enough times.

Taylor series are a piece of cake, I don't know what the big deal is... if you know how to derive, and understand how limits work, you shouldn't have a problem. Incidentally, Taylor series are a subset of the Laurent series which converges everywhere, even where Taylor series diverge. And if you guys think that high school calc is tough, wait till you get to university, a good time will be had by all

 

[Syringer]

Polar Coords were the worst. I never really learned how to find their intersection points and all.

I'm in multivariable calc now and that still stands to be the hardest thing I've heard to learn..which I use loosely.

 

[MisterNi]

The key to solving calculus problems is to have a clear picture of the problem before attempting it, I'll solve the problem given to start you off. Also note I haven't done calculus for a few years so if anyone sees a mistake, please correct me.

The problem states the surface area of the open ended box is 120cm^2 so we get our initial equation:

4xy (area of the sides of the box) + x^2 (area of the base of the box) = 120cm^2

now we need an equation for the Volume since that's what we're going to be maximizing (I believe this is considered an optimization, max/min problem)

Volume = yx^2 (Volume is height x base)

at this time, I don't believe you've learned how to deal with multi-variable differentials so you'll need to convert V into a single variable equation, so going back to our original equation:

4xy + x^2 = 120cm^2

solving for y gives you:
y = (120 - x^2)/4x

now plug y into our Volume equation:

=> V = (120x^2 - x^4)/4x

now that we have V in terms of x, we find what x needs to be to produce a maximum, but on an exam, you'll want to make sure you put limits on x since we're working with a variable that exists in space

so V = (120x^2 - x^4)/4x where 0< x <infinity

now we differentiate V to find our maximum value of x:

dV/dx = 30 - (3/4)x^2
=>x^2 = 40
x = 6.3246 (looks ok since x falls within 0<x<infinity)

now that we have x, we need to find y so we plug the value x we just found into our original equation:

4(6.2346)y + 40 = 120
y = 3.1423

so the dimensions 6.3246 x 6.3246 x 3.1423 would give the largest possible volume.

 

[Platypus]

because you touch yourself at night

 

[thawolfman]

You're just so pwnable!

 

[ManSnake]

because i am a kindergarten drop out :evil: