Calculus Question

[Xenon14]

If I have the following table
Days: 1,3,6,9,12,15
Temps: 20,31,28,24,22,21

How do I find/estimate the derivative at 12?

 

[SociallyChallenged]

I have NO clue!

 

[Heisenberg]

Maybe plot temps. vs days, find the slope of the line segments on either side of 12, and take the average?

 

[Martin]

try to put it in a function and derive it.

 

[LostHiWay]

What is ths Calculus day??? Why do they teach this stuff in schools?? Ohhh I forgot they need something to justify what they charge you.

If you ever need to use calculus in a REAL LIFE problem then you better fear for your job because you've F'd up somewhere.

 

[Martin]

<< Maybe plot temps. vs days, find the slope of the line segments on either side of 12, and take the average? >>






oh yeah, I totally forgot the graphical method. But who the hell uses that anyway?



Anyway, do as he told you. Plot all points, connect them in a smooth curve. Plot a tangent at point 12 and find its slop by extending it. use for formula slope = delta Y / Delta X.



That's a stupid question btw.

 

[Heisenberg]

<< What is ths Calculus day??? Why do they teach this stuff in schools?? Ohhh I forgot they need something to justify what they charge you.

If you ever need to use calculus in a REAL LIFE problem then you better fear for your job because you've F'd up somewhere. >>



I'll have to use it everyday assuming I get through grad school and get a job. And no, I don't think I fscked up somewhere.

Edit: Still undergrad right now.

 

[Martin]

hmm, you should get around -15/32

 

[Omegachi]

uh..... what are you learning right now? series?

yea....try plot it on a graph and then you'll find a function with the slope and then i don't know what to do after?

remember the derivative is the rate of change, and i don't know if that helps...

i am no help....

 

[Heisenberg]

<< hmm, you should get around -15/32 >>



You're drawing the tangent line and then estimating its slope? That wasn't really what I meant but that should work.

 

[RaynorWolfcastle]

<< What is ths Calculus day??? Why do they teach this stuff in schools?? Ohhh I forgot they need something to justify what they charge you.

If you ever need to use calculus in a REAL LIFE problem then you better fear for your job because you've F'd up somewhere. >>

That was one of the most ignorant comments I have ever heard

there are plenty of "real life" problems that use calculus. Take this: momentum is mass * velocity, energy is .5 mass times velocity squared <-- any idea how they are related? you know how many "real life" vehicles use this?

-Ice

 

[Yomicron]

<< hmm, you should get around -15/32 >>



because you are simply estimating, it is easier to do it graphically.

dx/dy between 9 and 12 = -2/3, between 12 and 15 = -1/3


take the average, you get -1/2

 

[RaynorWolfcastle]

well the best way would be to use linear algebra and fit a polynomial or use cubic splines. Then you could find an exact answer. May be a little more complex than the other though

-Ice

 

[LostHiWay]

<<

<< What is ths Calculus day??? Why do they teach this stuff in schools?? Ohhh I forgot they need something to justify what they charge you.

If you ever need to use calculus in a REAL LIFE problem then you better fear for your job because you've F'd up somewhere. >>

That was one of the most ignorant comments I have ever heard

there are plenty of "real life" problems that use calculus. Take this: momentum is mass * velocity, energy is .5 mass times velocity squared <-- any idea how they are related? you know how many "real life" vehicles use this?

-Ice >>



Thank You...You've proved my point.

Your thinking too hard...we have common sense that should kick in before we get to "a problem that needs calculus". It seems we're paying universities thousands of dollars to remove our common sense.

 

[Heisenberg]

<<

<<

<< What is ths Calculus day??? Why do they teach this stuff in schools?? Ohhh I forgot they need something to justify what they charge you.

If you ever need to use calculus in a REAL LIFE problem then you better fear for your job because you've F'd up somewhere. >>

That was one of the most ignorant comments I have ever heard

there are plenty of "real life" problems that use calculus. Take this: momentum is mass * velocity, energy is .5 mass times velocity squared <-- any idea how they are related? you know how many "real life" vehicles use this?

-Ice >>



Thank You...You've proved my point.

Your thinking too hard...we have common sense that should kick in before we get to "a problem that needs calculus". It seems we're paying universities thousands of dollars to remove our common sense. >>



You really need to quit while you're behind. :disgust:

 

[Xenon14]

Yeah, what I did was take the slope between 9 and 15 which is (y1 - y2) / (x1 - x2) which is (24-21) / (9-15) = - 1/2.

And as far as "not applying calc to real world" that's not true. Physics has a lot to do with calculus. Also a lot of applications about quantifying available area or volume, especially in objects that have no real definition. And I'm sure there are other uses but since I'm in BC Calc (Calc 1 & 2 college coarse for high school seniors) that's as far as my calc knowledge is at this point. Granted, for the average joe Algebra 1 will suffice, but Calc is interesting and definately something you should know regardless whether or not you'll use it.

 

[RaynorWolfcastle]

<<

<<

<<

<< What is ths Calculus day??? Why do they teach this stuff in schools?? Ohhh I forgot they need something to justify what they charge you.

If you ever need to use calculus in a REAL LIFE problem then you better fear for your job because you've F'd up somewhere. >>

That was one of the most ignorant comments I have ever heard

there are plenty of "real life" problems that use calculus. Take this: momentum is mass * velocity, energy is .5 mass times velocity squared <-- any idea how they are related? you know how many "real life" vehicles use this?

-Ice >>



Thank You...You've proved my point.

Your thinking too hard...we have common sense that should kick in before we get to "a problem that needs calculus". It seems we're paying universities thousands of dollars to remove our common sense. >>



You really need to quit while you're behind. :disgust: >>



LMAO, LostHiWay, do you have any idea why it's called "common sense" ? Let me know next time you build an engine using only common sense and no calculus. Do you have any idea how many of those equations spoon-fed to high-schoolers in physics and chemistry were derived using calculus?

Saying you don't like calculus is one thing, I can respect that. Saying that calculus is useless and shouldn't be taught is a whole different story.

-Ice

 

[Martin]

Xenon, the way you did it might not be correct. You took the average between 9 and 15. Average rate of change is different from what I did.

What I did was took the slope of the tangent at 12,. which yeilds the rate of change that instant, not the average.



LostHiWay, if indeed you are serious, I am glad there are people like you, as it allows smart people like me to make lots of money by exploiting you and others like you.



You may not like calculus, but we'd still be 1700s if it weren't for it.

 

[Zorba]

<< <<

<< What is ths Calculus day??? Why do they teach this stuff in schools?? Ohhh I forgot they need something to justify what they charge you.

If you ever need to use calculus in a REAL LIFE problem then you better fear for your job because you've F'd up somewhere. >>



That was one of the most ignorant comments I have ever heard

there are plenty of "real life" problems that use calculus. Take this: momentum is mass * velocity, energy is .5 mass times velocity squared <-- any idea how they are related? you know how many "real life" vehicles use this?

-Ice >>



Thank You...You've proved my point.

Your thinking too hard...we have common sense that should kick in before we get to "a problem that needs calculus". It seems we're paying universities thousands of dollars to remove our common sense. >>




If you really think that way, than you are a moron. You know even the simple equation for finding the volume of a cone came from Calculus? And just because somebody has already given us the easier equation doesn't mean that we don't still need calculus. In Physics I never use the Algebra equations because after you learn hundreds of them you tend to forget, I always just use a little calculus.

 

[MereMortal]

One way to solve a problem like this is to use discrete mathematics, such as finite differencing methods.

In this case the best we can do with 6 data points is a 5th-order equation for the derivative. The form of the equation is

df(i) = A*f(i-4) + B*f(i-3) + C*f(i-2) + L*f(i-1) + M*f(i) + N*f(i+1),

where df(i) is the 1st derivative of the function at point i, f(i) is the value of the function at point i and {A,B,...,N} are weighting coefficients to give the desired degree of accuracy (these are found through matching Taylor expansions to find a system of constraint equations, and then solving that system).

Many people here have been using a 2nd-order centered differencing scheme (whether they knew it or not ), where A=B=C=M=0, N=-L=1/(2*h) and h is the point spacing (in this problem, h=3 days). Then,

df(12) = (f(15) - f(9))/(2*3) + O(h^2) = -1/2 + O(h^2)


A higher-order scheme has A = 1/(20*h), B = -1/(3*h), C = 1/h, L = -2/h, M = 13/(12*h) and N = 1/(5*h).

This scheme gives df(12) = -13/30 + O(h^5), and is 5th-order accurate.


An nth-order accurate scheme just means that the derivative of a function of degree n or less will be solved exactly.