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!

Homework Help: Derivatives Problem

  1. Oct 27, 2008 #1
    Hey everyone, I'm a new Calculus student, and this problem on derivatives is giving me lots of trouble. I can't get around it! Please help.

    1. The problem statement, all variables and given/known data

    Find the coordinates of all points on the graph of y=1-x^2 at which the tangent line passes through the point (2,0).

    2. Relevant equations

    Possibly anything related to derivatives and slope, such as:
    y-y1 = m(x-x1)
    The power rule: nx^(n-1)

    3. The attempt at a solution

    All I know is the answer is: 2 (plus or minus) squareroot(3)
    I took the derivative of the original equation in the hopes that I might see where I should be going, but I'm just stuck. I don't see where the point comes in. If someone could tell me the steps of how to get the answer so I could use that knowledge in the future, I'd really appreciate it!
  2. jcsd
  3. Oct 27, 2008 #2


    User Avatar
    Science Advisor

    Okay, the derivative of y= 1- x2 is y'= -2x and that tells you that the slope of the tangent line, at x= x0 is -2x0.

    Write the equation of the staight line, with slope -2x0 that passes through (2.0). If the coordinates of a point at which that is the tangent line are (x0,y0), then they must satisfy both that equation and y'sub]0[/sub]
    = 1- x02. That gives you two equations for x and y.
  4. Oct 27, 2008 #3
    Hang on, I think I'm on the right track:

    y-y1 = m(x-x1) --> y = 2x-4

    And then make that equal to the derived equation?

    2x-4 = 1-x^2 ?

    Which should equal

    x^2 + 2x - 5 = 0 ?

    I put that in the quadratic formula, and I'm getting an answer that's close. Am I doing the math wrong?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook