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post #1 of 78 (permalink) Old 05-13-2009, 09:06 AM Thread Starter
 
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anyone good at calculus?

1. Let f(x, y) = 2x3 + y2 − 6x2 − 4y + 12x − 2.
(a) Find fx and fy.
(b) Find fxx, fxy, fyx and fyy.
(c) Find the critical points of f(x, y).
(d) Determine the relative extrema and saddle points, if any, of the function.


2. An open rectangular box is to be constructed from material that costs $3/ft2 for the bottom and $1/ft2 for its sides. Find the dimensions of the box of greatest volume that can be constructed for $36.



Free beer for the person who shows the work and answers all these questions correctly
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post #2 of 78 (permalink) Old 05-13-2009, 09:08 AM
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post #3 of 78 (permalink) Old 05-13-2009, 09:09 AM
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post #4 of 78 (permalink) Old 05-13-2009, 09:09 AM
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post #5 of 78 (permalink) Old 05-13-2009, 09:11 AM
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post #6 of 78 (permalink) Old 05-13-2009, 09:22 AM
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post #7 of 78 (permalink) Old 05-13-2009, 09:27 AM Thread Starter
 
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Only class I ever failed. Good luck.
I understand it ... I just have the issue of lack of time since I'm in Germany LOL
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post #8 of 78 (permalink) Old 05-13-2009, 09:29 AM
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(a)

fx = 6x^2+0-12x-0+2-0 = 6x^2-12x+2

Use the chain rule. d/dx(y^2) = 0, d/dx(-4y) = 0, d/dx(-2) = 0

fy = 0+2y-4+0-0 = 2y-4

Use the chain rule. d/dy(2x^3) = 0, d/dy(2x) = 0, d/dy(-2)

(b)

fxx = d/dx(fx) = d/dx(6x^2+2) = 12x-12

fxy = d/dy(fx) = d/dy(6x^2 + 2) = 0

d/dy(6x^2) = 0, d/dy(2) = 0

fyy = d/dy(fy) = d/dy(2y-4) = 2

I don't remember how to find the critical points of a multi variable function, I would have to look that up. But basically, you take the derivative and set that equal to zero and solve for X (in the single variable case). I'm sure its something similar. For extrema and saddle points, I don't remember that either. Would have to look it up.

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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.

Last edited by AgentofDarkness; 05-13-2009 at 11:02 AM.
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post #9 of 78 (permalink) Old 05-13-2009, 09:31 AM
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Originally Posted by AgentofDarkness View Post
(a)

fx = 6x^2+0-0+2-0 = 6x^2+2

Use the chain rule. d/dx(y^2) = 0, d/dx(-4y) = 0, d/dx(-2) = 0

fy = 0+2y-4+0-0 = 2y-4

Use the chain rule. d/dy(2x^3) = 0, d/dy(2x) = 0, d/dy(-2)

(b)

fxx = d/dx(fx) = d/dx(6x^2+2) = 12x

fxy = d/dy(fx) = d/dy(6x^2 + 2) = 0

d/dy(6x^2) = 0, d/dy(2) = 0

fyy = d/dy(fy) = d/dy(2y-4) = 2

I don't remember how to find the critical points of a multi variable function, I would have to look that up. But basically, you take the derivative and set that equal to zero and solve for X (in the single variable case). I'm sure its something similar. For extrema and saddle points, I don't remember that either. Would have to look it up.

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post #10 of 78 (permalink) Old 05-13-2009, 09:34 AM
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Someone is definitely still in school possibly taking that class right now...

As your attorney, I advise to you take this acid
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post #11 of 78 (permalink) Old 05-13-2009, 09:35 AM
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For part II

There are two equations.

V = w*l*h (volume of a box)
Cost = $36 = $3*(w*l) + 2*1*(w*h)+2*1*(w*l) (cost of bottom + cost of sides)

You have to maximize the volume equation, but I haven't figured out how to do that part yet. Its been a while.

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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.

Last edited by AgentofDarkness; 05-13-2009 at 09:38 AM.
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post #12 of 78 (permalink) Old 05-13-2009, 09:36 AM
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Someone is definitely still in school possibly taking that class right now...
Took that class my freshman year (2 years ago). I am now a junior. If I took that class in the Spring I probably would have solved both problems by now. I don't use this stuff too often.

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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.
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post #13 of 78 (permalink) Old 05-13-2009, 09:38 AM
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thats not calc I if you were doing calc III freshman year im surprised you failed it.
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post #14 of 78 (permalink) Old 05-13-2009, 09:38 AM
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Took that class my freshman year (2 years ago). I am now a junior. If I took that class in the Spring I probably would have solved both problems by now. I don't use this stuff too often.
Isn't that shit calc 3 at UIC? You took that froshie year?

As your attorney, I advise to you take this acid
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post #15 of 78 (permalink) Old 05-13-2009, 09:39 AM
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Isn't that shit calc 3 at UIC? You took that froshie year?
That is Calc III. I took it spring of my Freshman year. I didn't fail, I got an A.

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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.
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post #16 of 78 (permalink) Old 05-13-2009, 09:39 AM
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Isn't that shit calc 3 at UIC? You took that froshie year?
Its calc III everywhere / Some places even do diff eq with calce III
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post #17 of 78 (permalink) Old 05-13-2009, 09:40 AM
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That is Calc III. I took it spring of my Freshman year.
Calc 2 was the one that killed me. After Calc 2 I could do anything

That and I took Diff Eq at CLC (which was a toootal joke)

As your attorney, I advise to you take this acid
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post #18 of 78 (permalink) Old 05-13-2009, 09:41 AM
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Calc 2 was the one that killed me. After Calc 2 I could do anything

That and I took Diff Eq at CLC (which was a toootal joke)
My friend took Diff Eq at a community college. He doesn't know how to solve shit and he got an A.

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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.
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post #19 of 78 (permalink) Old 05-13-2009, 09:43 AM
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My friend took Diff Eq at a community college. He doesn't know how to solve shit and he got an A.
I took Dif Eq when I was at SIU and forgot everything as soon as I finished the final.

2.5 years as a ME and I haven't used any calculus. Thank god.

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post #20 of 78 (permalink) Old 05-13-2009, 09:43 AM
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my final was a take home final....

my Final!

As your attorney, I advise to you take this acid
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post #21 of 78 (permalink) Old 05-13-2009, 09:45 AM
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I took Dif Eq when I was at SIU and forgot everything as soon as I finished the final.

2.5 years as a ME and I haven't used any calculus. Thank god.
I always used to say, "Unless I'm in space without a computer or a graphing calculator forced to build a station, I'll never again use 97% of what I've learned in Calculus". I wish I could say the core concept is important, but I don't utilize most of that either, and even so, I'd have to relearn most of it.

As your attorney, I advise to you take this acid
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post #22 of 78 (permalink) Old 05-13-2009, 09:47 AM
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haven't seen that stuff since 2001...sorry

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post #23 of 78 (permalink) Old 05-13-2009, 09:48 AM
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So, do you guys use this stuff in real life a lot? Or, are any of you in real life yet? ?:
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post #24 of 78 (permalink) Old 05-13-2009, 09:48 AM
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I took Dif Eq when I was at SIU and forgot everything as soon as I finished the final.

2.5 years as a ME and I haven't used any calculus. Thank god.
I had to use multivariable calculus in the stats class I took last semester. I was doing LapLace transforms like crazy in my automatic control systems class. Integration/Differentiation pops up all the time in higher lever ECE classes.

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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.
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post #25 of 78 (permalink) Old 05-13-2009, 09:50 AM
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Quote:
Originally Posted by AgentofDarkness View Post
(a)

fx = 6x^2+0-0+2-0 = 6x^2+2

Use the chain rule. d/dx(y^2) = 0, d/dx(-4y) = 0, d/dx(-2) = 0

fy = 0+2y-4+0-0 = 2y-4

Use the chain rule. d/dy(2x^3) = 0, d/dy(2x) = 0, d/dy(-2)

(b)

fxx = d/dx(fx) = d/dx(6x^2+2) = 12x

fxy = d/dy(fx) = d/dy(6x^2 + 2) = 0

d/dy(6x^2) = 0, d/dy(2) = 0

fyy = d/dy(fy) = d/dy(2y-4) = 2

I don't remember how to find the critical points of a multi variable function, I would have to look that up. But basically, you take the derivative and set that equal to zero and solve for X (in the single variable case). I'm sure its something similar. For extrema and saddle points, I don't remember that either. Would have to look it up.
You can figure out the extrema and saddle points by pluggin in the formula into the TI-83.
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post #26 of 78 (permalink) Old 05-13-2009, 09:50 AM
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Quote:
Originally Posted by Mort82 View Post
So, do you guys use this stuff in real life a lot? Or, are any of you in real life yet? ?:
Yes. Take communication systems for instance. One way to demodulate an FM signal is to take the derivative of the FM signal and filter out the high frequency component. You don't actually do calculus though because you can use simulation/modeling software for most systems and avoid any actual calculations.

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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.
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post #27 of 78 (permalink) Old 05-13-2009, 09:50 AM
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Quote:
Originally Posted by AgentofDarkness View Post
I had to use multivariable calculus in the stats class I took last semester. I was doing LapLace transforms like crazy in my automatic control systems class. Integration/Differentiation pops up all the time in higher lever ECE classes.
Definitely while still in college they popped up all over the place. I'd say pretty much every 3/400 level engineering class, they came up.

Now that I'm in "real life" as Mort calls it, I haven't touched it. Guess that's one of the advantages to being a design engineer.

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post #28 of 78 (permalink) Old 05-13-2009, 09:51 AM
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Originally Posted by spetsnaz56 View Post
You can figure out the extrema and saddle points by pluggin in the formula into the TI-83.
TI-83s are for loosers. TI-89 is the only way I roll. This guy showed up to the stats final with a scientific calculator. I laughed at him.

Back to saddle points though, if you just put an answer you get a 0.

Quote:
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In motorcycle terms, that's like taking your Ducati to a dealer for service, and they hand you back a 1979 backfiring Honda 400 Hawk.. because after all, a bike is a bike.
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post #29 of 78 (permalink) Old 05-13-2009, 09:53 AM
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TI-83s are for loosers. TI-89 is the only way I roll. This guy showed up to the stats final with a scientific calculator. I laughed at him.
I had to work with what I had, but TI-89 definitely saves a lot of headaches.
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post #30 of 78 (permalink) Old 05-13-2009, 09:53 AM
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Wow....that looked really hard.

I'm having second thoughts about getting that ME degree now

and Ti-89 FTW. I love that calculator.

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