1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calc I derivatives, I know the answers, but how did I get there?

  1. Sep 7, 2010 #1


    User Avatar

    1. The problem statement, all variables and given/known data
    Question #2
    http://img830.imageshack.us/img830/8185/0000825.jpg [Broken]

    2. Relevant equations

    3. The attempt at a solution

    I can of course find the derivatives for both functions. When I set them equal to each other I get x=1/2 that's where the functions have parallel tangent lines for the same x value, however (I think that) the functions have parallel tangents everywhere, just at different x values. So I figured out that at any point x on x^2, there will be a parallel tangent from -x^2+2x-5 at 1-x

    I guess you have to find the equation of a tangent line that intersects with both graphs only once, no more no less, but I don't know how to write that out and solve for it. The answers are the tangent lines when x = -1 and 2 on x^2
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 7, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Label the point where the line intersects the upper parabola (a, a2) and the point where it intersects the lower parabola (b, -b2+2b-5). So those are two points on the line, and you also found that b=1-a. That should be enough to figure out the equation of the line, I think.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook