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 and Tangents

  1. Oct 1, 2007 #1
    1. The problem statement, all variables and given/known data
    Find equations of all tangent lines to the graph of [tex]y=4x^{3}+5x-8[/tex]
    3. The attempt at a solution
    I took the derivative of the equation, which was:


    I remember having done these types of questions in high school, but I just can't remember, and I can't find any questions which are similar. Urg!
  2. jcsd
  3. Oct 1, 2007 #2
    What does a derivative give you? You may be over-thinking this.
  4. Oct 2, 2007 #3
    Essentially you look at the points (x,4x^3+5x-8) on the curve and for each point associate a tangent line. That is, solve (y-y(x_0))=y'(x_0)(x-x_0) for y.
  5. Oct 2, 2007 #4
    It gives you the slope at any single point on a line.

    I thought I should use the [tex]12x^{2}+5[/tex], and the point [tex](1,-3)[/tex] in [tex]y=mx+b[/tex], to find a [tex]b[/tex] value, but when it's all said and done I don't get a tangent line. I get [tex]y=(12x^{2}+5)x-20[/tex] which just goes through the line.

    BTW, they're looking for a total of two equations for the answer.
  6. Oct 2, 2007 #5


    User Avatar
    Science Advisor

    It gives you the slope of the tangent line! Which is exactly what you want.
    And slope is a number not a formula in x. If you are looking for the slope of the tangent line at a point on the curve, you evaluate the derivative at the x value of that point.

    Your original question said "Find equations of all tangent lines". I THINK you are now saying "find equations for all tangent lines to 4x3+ 5x- 8 that pass through (1, -3)" but you never told us about that last part!
    One way to do that is not look at the derivative but look for solutions to the simultaneous equations y= m(x-1)+ 3 (any line through (1,3) can be written like that) and y= 4x3+ 5x- 8. For specific values of m that would give you a cubic for x which typically has three distinct answers. Look for the value of m so that equation has a double (or triple) root. That's how DesCartes found tangent lines "pre-calculus".
    Last edited by a moderator: Oct 2, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook