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  • Perplex
    IB Math AASL
    /
    Differentiation
    /

    Tangents and normals

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    Exercises

    Key Skills

    Tangents and normals

    Tangents and normals

    Definitions of tangent and normal, finding tangent and normal lines to a function

    Want a deeper conceptual understanding? Try our interactive lesson! (Plus Only)

    Exercises

    No exercises available for this concept.

    Practice exam-style tangents and normals problems

    Key Skills

    Tangent to f(x)
    SL 5.4

    ​L:mx+c​ is tangent to ​f(x)​ at ​x=a​ means

    ​
    same ysame y′​{f(a)=ma+cf′(a)=m​🚫
    ​

    Using point slope form the equation of the tangent is:

    ​
    y−f(a) ⇒y​=m⋅(x−a)🚫 =mx−ma+f(a)🚫​
    ​


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    Normal to f(x)
    SL 5.4

    The normal to ​f(x)​ at ​x=a​ is the line that passes through ​(a,f(a))​ and is perpendicular to the tangent:

    ​
    mn​⋅mt​=−1⇔mn​  ​=−mt​1​🚫 =−f′(a)1​🚫​
    ​

    Using point slope form the equation of the tangent is:

    ​
    y−f(a) ⇒y​=mn​⋅(x−a)🚫 =mn​x−mn​a+f(a)🚫​
    ​

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