Checking implicit differentiation answers?

[ktpr2]

How would you check your answer using a Ti86 for implicit diferentiation problems?

I was looking through some source code at ticalc.org and found this tidbit for an implict differentiation section:

(after given a point x and y, with function F1)

If der1(F1,y)==0
[exit]
else
(-der1(F1,x))/(der1(F1,y)) --> M
-M*x+y --> B

and it then displayed the slope M and the constant B as the tan line.

So, to check an answer, could I set y to some value, find x, and then treat the function as one variable and find the slope at point (x,y) by taking the derivativee of x with y equal to whatever set value and derivative of y with whatever x was found to be, in the equation -der(F1,x)/(der(f1,y) ? Does this make sense?

Also, shouldn't there be a way to use the point with the derivative i compute to check it's validity?

 

[ktpr2]

oh wait, hehe i can probably use Newton's method, if i have a point on the curve and a tangent equation to test out. Is this correct?

 

[ktpr2]

Figured it out. Not sure why but -dy/dx/dx/dy gives me the slope of implicit equations when i get a valid point. I whipped up a simple program for those like me who would like to check their answers:

http://www.ticalc.org/archives/files/fileinfo/367/36784.html