Post a New Question


posted by .

Find the equation of a tangent line of a graph pf y=x^2+4lnx, which is parallel to y=6x-3?

I know parallel lines have the same slope so the slope is 6 but I do not know how to find the b value.

  • Calc -

    Well you need to find where on that nasty function the slope is 6. Then at that (x,y) you write the y = 6 x + b that goes through that point.

  • Calc -

    how do I do this?

  • Calc -

    y = x^2 + 4 ln x
    dy/dx = slope = 2 x +4/x
    when is that slope 6?
    6 = 2 x + 4/x
    I get at x = 1 and at x = 2
    well 1 is easy because ln 1 = 0. It just said "a" tangent line, not all tangent lines.
    then y = 1
    so I am going to use (1,1)

  • Calc -

    I understand what you are saying but how do you do the algebra foe 6=2x+4/x I seem to have forgotten my algebra.

  • Calc -

    actually it's not so bad

    the derivative of your function is
    2x + 4/x
    setting this equal to 6 gave me a quadratic which factored nicely and had roots of
    x = 1 or x=2
    if x=1 then y = 1+4ln1
    y=1 ,
    so one case is m=6, point (1,1)

    case 2
    x=2, then y = 4 + 4ln2

    so m=6, point (2,4+4ln2)


  • Calc -

    All set now?

  • Calc -

    No i need help understanding the algebra behind solving 2x+4/x=6

  • Calc -

    multiply both sides by x
    6 x = 2 x^2 + 4
    2 x^2 - 6 x + 4 = 0
    1 x^2 - 3 x + 2 = 0
    (x-1)(x-2) = 0
    x = 1
    x = 2 are solutions.
    I used 1 so the point I could take was (1,1)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. MATH!

    What type of lines have a slope of zero? Write the equation of a line with the slope of -2 which contains the point (3,6) The x-axis has 0 slope. What about any other line with 0 slope?
  2. Algebra 1

    1. Which line is the flattest (or is less steep)?

    6. What happens to the graph of the line y = 3x -2 when the equation is changed to y = 3x +6?
  4. Algebra

    I'm suppose to write an equation with the following information: Line passes through (2,-6) and is parallel to x=8 I know i must use the slope point form the problem is that since x=8 I don not know which is the slope. Please help …
  5. math,correction

    The question asks: Find the slope of any ilne parallel to the line through points (20,9) and (7,8). so i found slope which i did: y=(9-8)/(20-7)= (-(-)/(13) so by having the slope how do find another the slope of any line parallel …
  6. Algebra

    'L' has y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1. (Instructions - write the equation of the line 'L' satisfying the given geometric conditions) We know that two lines that are parallel must have the same …
  7. math

    i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation …
  8. Algebra

    graph the equation x-3=y (where do I plot the points?
  9. Math

    1) What is the slope of a line that is parallel to y = 2?
  10. cal

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph …

More Similar Questions

Post a New Question