1. Not finding help here? Sign up for a free 30min 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!

Find the equation of the tangent to the curve

  1. Mar 23, 2005 #1
    Find the equation of the tangent to the curve [tex]y=x^3-7x^2+14x-8[/tex] at the point where [tex]x = 1[/tex]. [tex]\text{Answer: }y = 3x -3[/tex]
    Find the x-coordinate of the point at which the tangent is parallel to the tangent at [tex]x = 1[/tex].

    I need help on the second part.
     
  2. jcsd
  3. Mar 23, 2005 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, let x* be the point you seek.
    What do you know of x*?
    Do you agree that we must have y'(x*)=3?
    That is, the derivatives of y(x) must be equal at x=1 and x=x*
     
  4. Mar 23, 2005 #3
    Yes.
    I think I get it. But I still don't know how to get the answer.
     
  5. Mar 23, 2005 #4

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Well, do you agree that what you need to solve is the equation (written with "x"):
    [tex]3=3x^{2}-14x+14[/tex]
    This can be rewritten as:
    [tex]3(x+1)(x-1)-14(x-1)=0\to(3(x+1)-14)(x-1)=0[/tex]
    What must then x* be?
     
  6. Mar 23, 2005 #5
    Oh! Thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?