Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Courses » ap-calculus

Topic: [ap-calculus] Going crazy
Replies: 1   Last Post: Oct 10, 2012 9:08 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View  
Carl LaCombe

Posts: 10
Registered: 10/6/11
Re: [ap-calculus] Going crazy
Posted: Oct 10, 2012 9:08 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

NOTE:
This ap-calculus 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/getting-started
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 x-values.

I chose the first parabola to center on, since it has a simple equation,
and set the x-value 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 x-value 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 y-value of the tangent line at x_2 must equal the y-value 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 ap-calculus 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/getting-started
> 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+2x-5 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=ap-calculus





--
Carl LaCombe
Mathematics Teacher
The Cambridge School of Weston
45 Georgian Road
Weston, MA 02493
781-398-8322

---
To search the list archives for previous posts go to
http://lyris.collegeboard.com/read/?forum=ap-calculus



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.