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Math Help - Simple tangent/normal question

  1. #1
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    Simple tangent/normal question

    The curve C has equation y = x - 4x + 7. The point A has coordinates (1,4).

    a] Find the equation of the tangent to C at A.

    b] Find the equation of the normal to C at the point A.

    Now I'm pretty sure I differentiate the equation first to get 2x-4, but then I have no idea at all what to do after that. How is this done?
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  2. #2
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    Quote Originally Posted by db5vry View Post
    The curve C has equation y = x - 4x + 7. The point A has coordinates (1,4).

    a] Find the equation of the tangent to C at A.

    b] Find the equation of the normal to C at the point A.

    Now I'm pretty sure I differentiate the equation first to get 2x-4, but then I have no idea at all what to do after that. How is this done?
    Your considerations are OK.

    f(x)=x^2-4x+7 and f'(x)=2x-4

    Then the slope of the tangent in A is

    m_t=f'(4)~\implies~m_t = 4

    Then the perpendicular direction (the direction of the normal) is:

    m_{\perp}=-\dfrac1{m_t} ~\implies~m_{\perp} = -\dfrac14

    Use the point-slope-formula to determine the equation of the tangent:

    y-4=4(x-1)~\implies~y=4x

    Use the point-slope-formula to determine the equation of the normal:

    y-4=-\dfrac14(x-1)~\implies~y=-\dfrac14 x + \dfrac{17}4
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