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: Tangent's equation

  1. Nov 2, 2005 #1
    Decide an equation for the tangent to the curve y=6x-x^2 at the point (4,8)

    Well for this I thought I'd use this



    Then I thought I'd Use


    8-(-16)/8-4 =6

    Then I thought the answer was -6X - 16 But it Wasen't the answer should be
    -2x -16

    What am I doing wrong please help me!?
  2. jcsd
  3. Nov 2, 2005 #2


    User Avatar
    Science Advisor

    Yes, but you didn't need to do that- you were told that when x= 4, y= 8. That's what "at the point (4, 8)" means.
    NO! (4, 8) are not two different x- values: they are the (x,y) values of a single point.
    Basically, you are doing everything wrong! What you found was the equation of the line between the points (4, 8) and (8, -16).
    You were asked to find the equation of the line through the single point (4, 8) that is tangent to the curve there.

    I assume this is a calculus course, since otherwise there is no way to answer this question- but you didn't use any calculus!

    Do you know how to find the derivative of y with respect to x and evaluate it at x= 4?
    Do you know how "slope of the tangent line" is related to the derivative?
  4. Nov 2, 2005 #3
    That was no Help

    Yeah, I did know that the point was x1 = 4 And y1 = 8
    And I know I decide those things with f(x+h)-F(x) / h and so on but I doesn't help me nada. And your quotation didn't help me either please provide me a solution so maybe I understand?
  5. Nov 2, 2005 #4


    User Avatar
    Homework Helper

    Have you seen derivatives yet?
  6. Nov 2, 2005 #5


    User Avatar
    Homework Helper

    Izekid, you need to tell us about derivatives.
  7. Nov 2, 2005 #6
    You shall not know the derivate for the equation.... !
    Its a simple question where you shall DECIDE(you shall tell the one who does the question about what the equation shall be) the equation for the curve 6x-x^2
    And you have 2 coordinates (4,8)

    And The Answer Should be Y=-2x-16

    But if you want to derivate this it's gonna be
    X^2 = 2x^2-1

    6x - 2x = 4x And that's no answer

    So please help I have written the things that is written in my math book...
  8. Nov 2, 2005 #7
    Let f(x) = 6x-x^2
    therefore f'(x) = 6-2x. At point (4,8), f'(x) = -2. So, we say that the following is true...
    8-y = -2(4-x) => y = 16-2x (as required, I think)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook