How can i program my Ti-83 to graph a function?

Well right now im in Clac 1 and we're going over derivatives and itd sure be nice to be able to automatically graph the derivative of a certain function with the touch of a button. Now i have the equations to go about graphing this stuff up based off of a function already inputed, to get y1 hit the Vars button, y-vars, then functions,

(y1(x-.0001) - y1(x))/.0001

That function inputs two different values to though the first function (y1) and divides the results by .0001 which gives me the derivative.

The second derivate would be something like

(y2(x-.0001) - y2(x))/.0001

That takes the y2 function, the first derivative and pumps though 2 different x values, and divides the results by .0001

Now the problem i see here is that even though we can probably manage to graph the first derivative, i don’t see a way to get the second derivative since it cant really point to any particular y= equation.



Heres somewhat of a comment on getting the derivative on the calculator, but not quite part of the programming post.

Now a downside of this is it tends to be a bit slow, the first derivative is doing 3 equations for every calculation, and the second derivative is doing 5 equations for every calculation of the second derivative, i mean slow with a ti-83 silver (which is supposedly 2.5 times faster), so it would probably be unbearably slow on a normal ti-83.

So, your method for the first derivative is basically:

f'(x) = (f(x+d) - f(x))/d

where d = some "small" number. The similar equation for the second derivative is:

f''(x) = (f(x-d) - 2 f(x) + f(x+d))/d^2

Checking for f(x) = x^2:

f''(x) = ( (x-d)^2 - 2 x^2 + (x+d)^2 )/d^2
= 2 d^2 / d^2
= 2

Note that it is more accurate the smaller that you make d, but if you make it too small then you will hit the numerical accuracy of your calculator. So, experiment a little to find the best value.

You really don't have to program this... there is a built-in function to do what you need.

Strogian, Everyone ive talked to has said the ti-83 can not get the equation for a dirivitive, which would take away the need for what im doing, if you know how to do this could you please tell me how instead of telling me its "in my calculator"?

lochnesshamster, thanks for pointing out the intigration of the two formulas, and welcome to sharky forums :)





For clarity since ive probably clouded the waters with my first post

I know how to get the dirivitive of a function at a specific spot, what im wondering is how to graph a certain function, now this function happens to be a dirivitive, but that doesnt matter it could be how many dogs drop out of the sky onto the north pole per hour.

Well no, the 83 CAN'T get the equation for a derivative. I didn't think you wanted that. You seem to just want a graph of the derivative function.. that's what the little algorithm you put up does.

Anyway:

Y1=X^2+sin(X)+4
Y2=Deriv(Y1,X,X)

that will graph a function, and the derivative of it.
(I don't know if the thing is actually called Deriv().. it might be ADeriv() or something, I dunno.. that's why I wasn't specific in my post above.. Look in the math menu)

Quote:

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Originally posted by Strogian
Well no, the 83 CAN'T get the equation for a derivative. I didn't think you wanted that. You seem to just want a graph of the derivative function.. that's what the little algorithm you put up does.

Anyway:

Y1=X^2+sin(X)+4
Y2=Deriv(Y1,X,X)

that will graph a function, and the derivative of it.
(I don't know if the thing is actually called Deriv().. it might be ADeriv() or something, I dunno.. that's why I wasn't specific in my post above.. Look in the math menu)

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That would work out, the main reason i wanted to stick the other one inside a program was that it took so long to type out, thanks.

I invested in a TI89, and its been the best thing i have ever bought.
its expensive, but worth it, even if you own an 86 or 83, its sitll worth upgrading for the money.

Quote:

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Originally posted by lms
I invested in a TI89, and its been the best thing i have ever bought.
its expensive, but worth it, even if you own an 86 or 83, its sitll worth upgrading for the money.

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The problem comes in when you take classes where the teachers wont let you use an 89 because its too powerful.

Price wise a ti-83 silver is just about the same as a ti-89, it has a faster CPU and more memory.

after doing calc 1-3 in college, i've never had a professor tell me i "cant" use my 89, its just that they ask you to show work :P

Quote:

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Originally posted by JGC84
after doing calc 1-3 in college, i've never had a professor tell me i "cant" use my 89, its just that they ask you to show work :P

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You dont have some of the profs i do at my school :o

math = teh suck

ti89 is a neat toy.

I love especially how it does integration by parts, and shows u everything : P


Though, any real calc class would never, ever let u use a calculator on an exam...

When I take multivariable next semester, im gonna be lovin that ti89.