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 February 6th, 2012, 06:06 AM #1 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Equation of the tangent line Hi! I need to find dy/dx explicitly (i.e. in the form dy/dx=g(x,y) if x^3+y^2+2y=2. Then I need to determine the equation of the tangent to the curve represented by the above equation at the point (-1,1). Can anyone help? Thanks February 6th, 2012, 06:30 AM #2 Global Moderator   Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5 Re: Equation of the tangent line This is called "implicit differentiation", since you haven't/won't solve for y explicitly before differentiating. x^3+y^2+2y=2 We are going to use the chain rule on EVERY TERM. I will write dx/dx, just so you can see that the chain rule is always in play. However, dx/dx is just equal to 1, so we will make the appropriate simplification... (x^3) ' + (y^2) ' + (2y) ' = (2) ' ......here I have just put a ' after every term to indicate that we are differentiating. (3x^2 dx/dx) + (2y dy/dx) + (2 dy/dx) = 0 ... chain rule, power rule, and/or constant rule Factor out the dy/dx and simplify... (3x^2) + (dy/dx)*(2y + 2) = 0 Solve for dy/dx... (dy/dx)*(2y + 2) = -3x^2 after dividing. Plug in x = -1, y = 1 to THIS formula to get the slope at the point (-1, 1). Then use point slope formula to get an equation of the tangent line. February 6th, 2012, 06:36 AM #3 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Equation of the tangent line Thanks, I thought that. Can you please help me with the point slope formula. February 6th, 2012, 07:05 AM #4 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Equation of the tangent line Actually Is the following correct, plug in x=-1 and y=1, i get the slope m = -3/4 using the point slope fomula i get y-y1=m(x-x1) y-1=-3/4(x--1) y=-3/4x+1/4 February 6th, 2012, 07:24 AM #5 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Equation of the tangent line Yes, that is correct.  February 9th, 2012, 01:29 AM #6 Member   Joined: Jan 2012 Posts: 82 Thanks: 0 Re: Equation of the tangent line Thank you for your help  Tags equation, line, tangent Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post math999 Calculus 4 February 25th, 2013 07:36 PM unwisetome3 Calculus 2 October 28th, 2012 06:52 PM unwisetome3 Calculus 4 October 20th, 2012 07:38 AM kevpb Calculus 3 May 25th, 2012 10:32 PM RMG46 Calculus 28 September 28th, 2011 09:21 AM

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