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Math Help - How to find a point in a Equation

  1. #1
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    How to find a point in a Equation

    Curve C has equation
    y=x^3+x^2-5x+3

    there are two points on C where the gradient of the tangent to C is equal to 3.
    Find the x coordinates of these two points.

    Can you pls explain it to me clealry! Thank u very much
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  2. #2
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    Quote Originally Posted by thereddemon View Post
    Curve C has equation
    y=x^3+x^2-5x+3

    there are two points on C where the gradient of the tangent to C is equal to 3.
    Find the x coordinates of these two points.

    Can you pls explain it to me clealry! Thank u very much
    Take the first derivative and set f'(x) to 3.

    f'(x) = 3x^2 - 5 = 3 \rightarrow f'(x) = 3x^2 - 8 = 0

    solve using the difference of two squares:

    (\sqrt3 - 2\sqrt2)(\sqrt3 + 2\sqrt2) = 0

    so x = \frac{2\sqrt2}{\sqrt3} or x = -\frac{2\sqrt2}{\sqrt3}
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