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Re: [apcalculus] Going crazy
Posted:
Oct 10, 2012 9:08 PM


NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and post messages there.  Rebecca,
The way I saw to do this, it is a challenging problem. The issue is that the slopes are equal at the lines points of tangency with the parabolas, but those don't happen at the same xvalues.
I chose the first parabola to center on, since it has a simple equation, and set the xvalue of the point of tangency to the first parabola as x_1. This means that the point of tangency is (x_1, x_1^2) and the slope is 2*x_1. I set the xvalue of the point of tangency to the second parabola as x_2. I found the equation of the tangent line using the slope and point of tangency to the first parabola.
Then I get two equations in the two unknowns, x_1 and x_2. The first is from knowing that the derivatives of the first parabola at x_1 and of the second parabola at x_2 must be equal. The second one is from knowing that the yvalue of the tangent line at x_2 must equal the yvalue of the second parabola. Once you solve these two equations for x_2 and x_1 then you can get the equations of the tangent lines.
Perhaps there is a more intuitive way, but this one works.
Carl
On Wed, Oct 10, 2012 at 4:41 PM, Rebecca Tackett < rtackett@evansvilledayschool.org> wrote:
> NOTE: > This apcalculus EDG will be closing in the next few weeks. Please sign up > for the new AP Calculus > Teacher Community Forum at > https://apcommunity.collegeboard.org/gettingstarted > and post messages there. > >  > I need some help with this problem. What am I missing? > > > Graph the two parabolas y=x^2 and y=x^2+2x5 in the same coordinate > plane. Find the equations of the lines that are simultaneously tangent to > both parabolas. I can visualize where the two equations are but now I can?t > figure out how to write their equations? > > I keep setting the derivatives equal to each other as the slopes of the > same linear equation and solved for x and got x=0 and x=.5, but I don't > think that's correct. And I can't figure out how to write the equation at > either of those points so that it is tangent simultaneously. Any thoughts? > The problem is from Larson 4e, p.201 #2 > > Thanks, > Rebecca Tackett > Upper School Mathematics Instructor > Evansville Day School > >  > To search the list archives for previous posts go to > http://lyris.collegeboard.com/read/?forum=apcalculus
 Carl LaCombe Mathematics Teacher The Cambridge School of Weston 45 Georgian Road Weston, MA 02493 7813988322
 To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus



