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Math Help - tangent line problems

  1. #1
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    tangent line problems

    a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

    b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)
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  2. #2
    Super Member TheChaz's Avatar
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    re: tangent line problems

    Use the point slope formula...

    y - y_1 = m(x - x_1)

    The point (x_1 , y_1) = (5, -3)

    The slope is 4.
    Thanks from angelamonique
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  3. #3
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    re: tangent line problems

    Quote Originally Posted by angelamonique View Post
    a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

    b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)
    The tangent line at (x_0,g(x_0)) is y-g(x_0)=g'(x_0)(x-x_0)~.
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    re: tangent line problems

    Thank you, but can you also tell me how you figured that out?
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    Re: tangent line problems

    They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.
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  6. #6
    Super Member TheChaz's Avatar
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    Re: tangent line problems

    Quote Originally Posted by HallsofIvy View Post
    They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.
    I wasn't sure exactly how to approach that!

    Indeed, the veracity/validity/whatever of the point slope formula should not be called into question at this juncture. So we're left with the task of finding a point and a slope, in order to determine the desired line.
    Welp, g(5)=-3 means that (5, -3) is the point.
    And you really DO need to know that the slope of the tangent is given by the derivative.
    Thanks from angelamonique
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