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Math Help - Equation of a Tangent

  1. #1
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    Equation of a Tangent

    The tangent to the curve y = px^3 at the point A where x=2, meets the y-axis at B(0,8). Find the gradient of the curve at point A.

    I have attempted using differentiation and found the gradient to be 12p... However, gradient must be in value form..
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  2. #2
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    Quote Originally Posted by Punch View Post
    The tangent to the curve y = px^3 at the point A where x=2, meets the y-axis at B(0,8). Find the gradient of the curve at point A.

    I have attempted using differentiation and found the gradient to be 12p... However, gradient must be in value form..
    hi

    At x=2 , y=p(2)^3=8p so the tangent touches the curve at (2,8p)

    gradient of tangent = (8p-8)/2

    so 8p-8/2=12p ..
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  3. #3
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    I already did this in my attempt... The gradient MUST be in value form.
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  4. #4
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    Quote Originally Posted by Punch View Post
    I already did this in my attempt... The gradient MUST be in value form.
    look closer , \frac{8p-8}{2}=12p , solving this , p=-1/2 so

    dy/dx=12p=12(-1/2)=-6
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