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Find equation of line that is perpendicular to the tangent line to the curve

  1. Aug 3, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the equation of the line that is perpendicular to the tangent line to the curve, y=(3x+1)/(4x-2) at the point (1,2)

    2. Relevant equations



    3. The attempt at a solution
    I am absolutely confused with this problem. I tried taking a derivative of the equation. And I got y'=-10/(4x-2)2
    I couldn't set it equal to 0, it will not work. What have I done wrong?
     
  2. jcsd
  3. Aug 3, 2010 #2
    There's no need to solve -10/(4x-2)2 = 0 because you're not supposed to find when/if the tangent line to the curve is ever horizontal. The problem wants you to first find the slope of the tangent line at the point (1, 2); you need to find the derivative when x = 1.
     
  4. Aug 4, 2010 #3
    Excuse me, what exactly do you mean by that?
     
  5. Aug 4, 2010 #4

    Dick

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    y'(x) is the slope of the tangent line. Substitute x=1 into your equation for y'(x) to find the slope of the tangent line. What's y'(1)? Now what's the relation between the slope of the tangent line and a perpendicular to it?
     
  6. Aug 5, 2010 #5
    OK, here we go:

    y'(1)=-10/4

    Normal line is reciprocal of the tangent, which is 4/10.
    The normal line equation is:

    y-2=0.4(x-1)
    y=0.4x+1.6
     
  7. Aug 5, 2010 #6

    Dick

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    Uh, NEGATIVE reciprocal of the tangent. Works for me. Seem ok to you?
     
  8. Aug 5, 2010 #7
    That's what I exactly meant :))
    Thank you SO much for everything.
     
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