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Find the slope of the tangent line using a specific formula

  1. Dec 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the slope of the tangent line using a specific formula

    g(x)=3t-t2

    at (0,0)

    2. Relevant equations

    Im told to use this equation by the book
    f(c+deltax) - f(c)
    Deltax

    3. The attempt at a solution
    Everytime i plug it in by way of the books style i get 2c. and then you are supposed to plug in the x value which gives me 0. But the right answer is 3
     
  2. jcsd
  3. Dec 13, 2009 #2
    Perhaps if you show some of your algebra...
     
  4. Dec 13, 2009 #3
    sorry.

    yeah im not so sure its an aritmetic mistake but a misunderatanding of how to do things. but following what the book said to do here goes,

    f(c + deltax) - f(c)
    delta x

    ((c + deltax)2 - 3t) - (c2 -3t) foil it out
    delta x

    2c(deltax) + (deltax)2 simplify
    Delta x

    and then my book gets rid of both of the delta x's
    i assume by simplyfying and i can only assume the deltax2 by plugging in zero because the lim approaches 0


    and i get the wrong answer because i end up with 2c (which the book says to do) and then plug in a point which is 0 and its supposed to end up being 3?
     
  5. Dec 13, 2009 #4
    You're getting the wrong answer because [tex]f(c + \Delta x) \neq ( c + \Delta x )^2 - 3t[/tex]. You should think about why.
     
  6. Dec 13, 2009 #5
    thats the problem the book gives an example for linear problems, eg y= x and parabolas, y=x^2

    im not sure what to do with this?
     
  7. Dec 13, 2009 #6
    This isn't anything that would be an example in a calculus book, because it's function evaluation. (Although it may be in one of the "introductory" sections.)

    If you have a function f(t) what does [tex]f(c + \Delta x)[/tex] mean? It means everywhere in the definition of f that you see a t, you should put a [tex]c + \Delta x[/tex].
     
  8. Dec 13, 2009 #7
    really? its in chapter two of my calculus book section 2.1 finding the slope for a tangent line.

    so your saying it should look like

    3(c + Delta x) - (c + Delta x)2

    so

    3c + 3Delta x - c2 + 2c(deltax) + (deltax)2

    ?
     
  9. Dec 13, 2009 #8
    I know this problem is a calculus problem, I'm saying the issue you're having isn't a calculus issue, so it might not be addressed in the examples.

    Yes. You need to put [tex]c + \Delta x[/tex] everywhere you see t. Now do some algebra to simplify...
     
  10. Dec 13, 2009 #9
    oh okay i understand what your saying about what im doing wrong. i realize that f(x) is meant to plugged in whenever you see x. but the formulas was throwing me off.

    but is this over delta x like the equation?
     
  11. Dec 13, 2009 #10
    Yes, the definition of derivative stays the same.
     
  12. Dec 13, 2009 #11
    so you can cancel a single delta x right? what happens with the other delta x's i assume the best one to cancel is the 2c delta x

    sorry i know im making this harder than it should be.....
     
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