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Math Help - Find the equation of tangent line

  1. #1
    DBA
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    Find the equation of tangent line

    Hello,
    I need to find the tangent line to the grapg of y=g(x) at x=5 if g(5) = -3 and g'(5) = 4

    Can anybody give me a hint how I can do that?
    Thanks
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  2. #2
    MHF Contributor

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    Quote Originally Posted by DBA View Post
    Hello,
    I need to find the tangent line to the grapg of y=g(x) at x=5 if g(5) = -3 and g'(5) = 4
    The tangent line to the graph of y=g(x) \text{ at } x_0 is y-g(x_0)=g'(x_0)(x-x_0).
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  3. #3
    DBA
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    So,
    y-g(5)=g'(5)(x-5)
    y+3=4(x-5)
    y+3=4x-20
    y=4x-23

    Is that correct?
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  4. #4
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    that is correct.

    The equation for a line can be written like y=kx+c

    g'(5)=4 gives you the slope of the line (k)

    and g(5)=-3 gives you a point in the tangent line (x and y)

    Knowing that,

    -3=4*5+c
    -3=20+c
    c=-23

    y=4x-23
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