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Math Help - Graphing the curve and both tangents...

  1. #1
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    Graphing the curve and both tangents...

    QUESTION:

    (a) Find the slope of tangent to the curve y=3+4x^2-2x^3 at the point where x=a.
    (b) Find equations of the tangent lines at the points (1,5) and (2,3).
    (c) Graph the curve and both tangents on a common screen.


    My answers:

    (a) m(TL) = dy/dx = 8x-6x^2

    (i) at P(1,5); m(TL) = 2
    (ii) at P(2,3); m(TL) = -8

    (b)

    (i) y = 2x +3
    (ii) y = -8x+19

    (c) now in this part of graphing i don't know how to graph the curve since it is raised to cube..i don't know either what kind of curve is this..

    ^_^
    Last edited by cutiemike1; August 21st 2010 at 08:12 PM.
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  2. #2
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    A method that always works is to put in points for the x to solve for the y to plot on your graph.
    Eg.
    If x = -0.5, then y = 4.25
    If x = 0, then y = 3
    If x = 0.5, theny = 3.75
    And then join up the dots

    Here's a common image of a cubic graph generated by Wolfram|Alpha:



    Your graph should look something like this one, maybe moved up a bit.
    Then just add the tangent lines to your graph for the 2 tangent lines.
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  3. #3
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    oh yeah!.. like test points.. thanks a lot ^_^
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  4. #4
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    Quote Originally Posted by cutiemike1 View Post
    QUESTION:

    (a) Find the slope of tangent to the curve y=3+4x^2-2x^3 at the point where x=a.
    (b) Find equations of the tangent lines at the points (1,5) and (2,3).
    (c) Graph the curve and both tangents on a common screen.


    My answers:

    (a) m(TL) = dy/dx = 8x-6x^2
    Strictly speaking, this is wrong. The problem asked for the derivative " at the point where x=a." The correct answer would be dy/dx= 8a- 6a^2.

    (i) at P(1,5); m(TL) = 2
    (ii) at P(2,3); m(TL) = -8
    Except to solve part (b) there were no parts "i" and "ii". You were not asked for the slope of the tangent at x= 1 and x= 2 in part (a),

    (b)

    (i) y = 2x +3
    (ii) y = -8x+19

    (c) now in this part of graphing i don't know how to graph the curve since it is raised to cube..i don't know either what kind of curve is this..

    ^_^
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  5. #5
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    1. So does that mean, i cannot get the slopes given two points, it's because of "x=a"?
    2. It is just a guide for me to know where the slope is leaning.
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