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Integration, Differentiation, Stationary Points etc help please (: watch

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    Could I please have some guidance on this question?


    Curve has equation y = 2x^3-6x.

    (i) Show that the curve crosses the x-axis at the origin and the points (Sqrt3,0)
    and (-Sqrt3,0)

    (ii) Find dy/dx and stationary points on curve

    (iii) Find d^2/dx^2 and stationary points

    Thanks in advance
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    For the first question what is the value of y at the x-axis?

    What do you know about the value of dy/dx at a stationary point? And what does the value of d^2y/dx^2 at a stationary point represent?
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    (Original post by Ben121)
    For the first question what is the value of y at the x-axis?

    What do you know about the value of dy/dx at a stationary point? And what does the value of d^2y/dx^2 at a stationary point represent?
    I haven't been told what the value of y at the x-axis is; only the co-ordinates. Also for them both; need to find f(x) and f'(x).
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    (Original post by cee.jay)
    I haven't been told what the value of y at the x-axis is; only the co-ordinates. Also for them both; need to find f(x) and f'(x).

    At the x-axis the value of y is 0. Put that into your equation to work out what x is.
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    (Original post by cee.jay)
    I haven't been told what the value of y at the x-axis is; only the co-ordinates. Also for them both; need to find f(x) and f'(x).
    At the x axis y=0, so substitute that into the equation to get 0 = 2x^3-6x, then bring 6x to the other side to get 2x^3 = 6x, then find the values of x for which this is true

    Spoiler:
    Show
    (obviously 0 is one of them, the other is x^3 = 3x or x^2 = 3, hence x = sqrt(3))).


    The second part is just a simple differentiation, and to find the stationary points you set the derivative to 0 (since you are finding the points on the curve at which the gradient is 0 and the gradient is found by differentiation) and again find values of x which satisfy this, then for part 3 you simply take the derivative again. What does it mean by the stationary points of d^2y/dx^2 though? Does it want you to find the nature of the stationary points found in part ii)?
 
 
 
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