Implicit Differentiation

Date: 11/4/96 at 12:29:14
From: Scott Thompson
Subject: Implicit Differentiation

Here's my question:

Find the slope of the tangent at the point (3,4) on the circle 
x^2 + y^2 = 25.

My answer: I guess we would need to put it in the y = mx + b form. 

Thanks for any help,
Scott

Date: 11/05/96
From: Doctor Pete
Subject: Re: Implicit Differentiation

To find the slope of the tangent at the point (3,4) on the circle 
x^2 + y^2 = 25 you need to use implicit differentiation.  You cannot 
put a circle into the form of a line.  In particular, you want to find 
dy/dx:

     d/dx[x^2 + y^2 = 25] ==> 2x + 2y dy/dx = 0.

Can you complete the solution?

-Doctor Pete,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/