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Re: [apcalculus] Going crazy
Posted:
Oct 10, 2012 8:56 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.  On 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 >
A nice problem.
First of all, set the slopes equal to each other: 2x = 2x + 2 and get x = 1/2. Hold that aside for awhile,
Consider y = x^2. The slope = 2x. At some point (a, a^2), the equation of the tangent line will be y  a^2 = 2a (x  a) or y = 2ax  a^2.
Consider y = x^2 + 2x  5. The slope = 2  2x. At some point (a, a^2 + 2a  5), the equation of the tangent line will be y  (a^2 + 2a  5) = (2  2a)(x  a) or y = 2x  2ax + a^2  5
Now use the x = 1/2 and set the equations equal to each other: a  a^2 = 1  2a + a^2  5 which simplifies to a^2  a  2 = 0. Solve and you get a = 2 or a = 1:
At a = 2: the equation line is y = 4x  4
At a = 1, the equation line is y = 2x + 1
Stu Schwartz www.mastermathmentor.com
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