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Topic: [ap-calculus] Going crazy
Replies: 2   Last Post: Oct 10, 2012 11:39 PM

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Posts: 6
From: Hagerstown, MD
Registered: 6/28/11
Re: [ap-calculus] Going crazy
Posted: Oct 10, 2012 8:18 PM
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This ap-calculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus
Teacher Community Forum at
and post messages there.
Hi Rebecca,

x=.5 is correct. When you differentiate you get 2x and -2x+2, set them
equal to get x=.5. So they both have tangents with slope 1 at x=.5. You
can then get equations


As far as the x=0 goes, if you look at the graph, y=x^2 has a horizontal
tangent at x=0 while the other parabola does not, so this cannot be an

Hope this helps!

Joellen Cope
Saint James School
Hagerstown, MD

On 10/10/12 4:41 PM, "Rebecca Tackett" <>

>This ap-calculus EDG will be closing in the next few weeks. Please sign
>up for the new AP Calculus
>Teacher Community Forum at
>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
>can¹t 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
>Rebecca Tackett
>Upper School Mathematics Instructor
>Evansville Day School
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