Checking implicit differentiation answers?

In summary, to check if an answer is correct for implicit differentiation problems using a Ti86, one can use the formula (-der1(F1,x))/(der1(F1,y)) to find the slope at a given point (x,y) and compare it to the slope given by the tangent line equation. Additionally, one can use Newton's method to test for validity by plugging in a point on the curve and the tangent equation. There is also a program available on ticalc.org for this purpose.
  • #1
ktpr2
192
0
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?
 
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  • #2
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?
 
  • #3
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
 

Related to Checking implicit differentiation answers?

What is implicit differentiation?

Implicit differentiation is a mathematical technique used to find the derivative of a function that is not explicitly defined in terms of one variable. This is often used when the function is defined implicitly by an equation.

Why is it important to check implicit differentiation answers?

Checking implicit differentiation answers is important because it helps to ensure that the calculated derivative is correct. This is especially important in more complex problems where there may be multiple steps involved in the differentiation process.

What are some common mistakes to look out for when checking implicit differentiation answers?

Some common mistakes when checking implicit differentiation answers include using the wrong chain rule, forgetting to apply the product or quotient rule, and making errors in algebraic simplification.

How can I check my implicit differentiation answers?

One way to check your implicit differentiation answers is to plug the calculated derivative back into the original equation and see if it satisfies the equation. Another way is to compare your answer to the solution obtained through a different method, such as using the explicit form of the function.

What are some tips for checking implicit differentiation answers?

Some tips for checking implicit differentiation answers include double-checking the steps in your differentiation process, being careful with algebraic simplification, and using multiple methods to verify your answer. It can also be helpful to work through the problem again to see if you get the same answer.

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