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    The points P(x,y) and Q(x+dx,y+dy) lie on the curve y=3x^2 +2
    a) Show that the gradient of the chord PQ is (3(x+dx)^2 - 3x^2)/ dx.
    d= delta
    so far I have the gradient as y+dy-y/x+dx-x
    I then substituted this into y=3x^2+2
    y+dy=3(x+dx)^2+2
    I'm really unsure of what to do next


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    (Original post by imaan2121)
    The points P(x,y) and Q(x+dx,y+dy) lie on the curve y=3x^2 +2
    a) Show that the gradient of the chord PQ is (3(x+dx)^2 - 3x^2)/ dx.
    d= delta
    so far I have the gradient as y+dy-y/x+dx-x
    I then substituted this into y=3x^2+2
    y+dy=3(x+dx)^2+2
    I'm really unsure of what to do next


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    well you know the gradient will be  \displaystyle \frac{dy}{dx} since that is the value of  \displaystyle  \frac{\text{change in y}}{\text{change in x}}

    using P and Qs coordinates and putting them into the curve gives you two equations

    1)  \displaystyle y = 3x^2 + 2

    2)  \displaystyle y + dy = 3(x+ dx)^2 +2

    can you go from here?

    Spoiler:
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    find dy in terms of x and dx
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    (Original post by DylanJ42)
    well you know the gradient will be  \displaystyle \frac{dy}{dx} since that is the value of  \displaystyle  \frac{\text{change in y}}{\text{change in x}}

    using P and Qs coordinates and putting them into the curve gives you two equations

    1)  \displaystyle y = 3x^2 + 2

    2)  \displaystyle y + dy = 3(x+ dx)^2 +2

    can you go from here?

    Spoiler:
    Show


    find dy in terms of x and dx

    How did you get 2)?
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    (Original post by imaan2121)
    How did you get 2)?
    subbed Qs coordinates into the curve equation since it lies on the curve
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    (Original post by DylanJ42)
    subbed Qs coordinates into the curve equation since it lies on the curve
    Ah ok thankyou. I understand it up to this point, but still unsure of what to do next
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    (Original post by imaan2121)
    Ah ok thankyou. I understand it up to this point, but still unsure of what to do next
    well you can find dy in terms of x and dx now, since you have an equation for y, just make a sub

    also as you said in your OP,  \displaystyle \text{gradient} = \frac{(y + dy)- y}{(x + dx) - x} so sub in 1) and 2) in place of y and (y+dy) respectively
 
 
 
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