2. Gradient of a Chord & First Derivative

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    GRADIENT OF A CHORD

    0

     P 

    Q

     y = f(x)

     

     y

     x

    Gradient of chord PQ =

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    0

     P 

     

     y = f(x)

     

     y

     x

    GRADIENT OF THE TANGENT TO THE CURVE AND THE FIRT DERIVATIVE OF A FUNCTION

      As the point Q  moves nearer and

    nearer to the point  P  such as ….as

    shown in the diagram, the chord

     PQ can be seen getting nearer andnearer to the tangent at point P.

     

    = gradient of tangent to thecurve at point P

     Therefore

    ,

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    0

     P 

     

     y = f(x)

     

     y

     x

     

    Then, gradient chord P !

    As point approaches point P, , therefore

    sma"" change in y

    sma"" change in x

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    = gradient of tangent to

    the curve at point P

    #n ca"cu"us , we denote as

    $ence represent s the gradient of tangent at a point P  on

    the curve

    is a"so %nown as the first derivative of the function


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