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Tangent line problem

  1. Oct 29, 2011 #1
    I'm on mobile so I can't use latex.

    Let C: y=8x^5+5x+1 and suppose L is a line through the origin tangent to C at a point P=(a,f(a)) on C.

    -Find the coordinates of P

    -Compute the slope m sub L of L

    Where should I begin? I'm guessing I would need the derivative of the equation f(x)? Then I would use the point slope form to figure out point P?
  2. jcsd
  3. Oct 29, 2011 #2


    Staff: Mentor

    Maybe a sketch of the function?
    One would think that might somehow enter into things.
  4. Oct 29, 2011 #3
    After I sketch the eqiation what would I do after? So does that mean L is a secant line through the equation?
  5. Oct 29, 2011 #4


    Staff: Mentor

    L is a line that is tangent to the graph of the function. It's not a secant line (a line that hits a curve at two points).

    BTW, "a secant line through the equation" doesn't make much sense, unless you actually draw a line through an equation, as opposed to drawing a line through the graph of an equation.
  6. Oct 29, 2011 #5
    Haha I'll be more precise. I misread I thought it was going through the graph of the equation thinking its a secant line.

    So I got the derivative which is f'(x) = (40x^4) + 5.

    I wouldn't be able to apply the slope formula since I'm figuring out the coordinates of P. What methods are there?
  7. Oct 29, 2011 #6


    Staff: Mentor

    So you have a line from (0, 0) to (a, f(a)) on the graph of your curve. Write an expression that represents the slope of the line.

    Write another expression that represents the slope of the tangent at any point on your curve.

    Equate the two expressions.
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