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    Given that y=\frac{1}{3} x^3 - 9x is the equation of the curve.
    24x+3y+2=0 is the equation of the tangent to the curve at the point(x,y), find x and y.

    I differentiated this and found that x must equal +1 or -1. Then i found that the gradient of the tangent is -8 by dividing by 3. So can someone tell what method should i use to find the answer? Please dont give actual solutions
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    When you differentiate the equation of the curve what expression do you get.
    The coordinates x and y are the point where the gradient of the tangent is equal to the gradient of the curve at that point. You've correctly worked out the gradient of the tangent and the gradient to the curve is the differentiation of the equation of the curve. You just need to make an equation to find x and then find y.

    I'm not sure what you mean when you say x must be equal to +1 or -1.
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    (Original post by Chelsea12345)
    Given that y=\frac{1}{3} x^3 - 9x is the equation of the curve.
    24x+3y+2=0 is the equation of the tangent to the curve at the point(x,y), find x and y.

    I differentiated this and found that x must equal +1 or -1. Then i found that the gradient of the tangent is -8 by dividing by 3. So can someone tell what method should i use to find the answer? Please dont give actual solutions
    Right so the cubic has the gradient of -8 at x=\pm 1 and you need to figure out at which one of those points the line 24x+3y+2=0 is tangent at.

    The way to do this is to work out the values of x=\pm 1 on the cubic and then plug those pairs of results, (x,y) coordinates, into the line equation to see which one works because one of the won't for obvious reasons. Whichever one satisfies the line equation is your point.
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    (Original post by RDKGames)
    Right so the cubic has the gradient of -8 at x=\pm 1 and you need to figure out at which one of those points the line 24x+3y+2=0 is tangent at.

    The way to do this is to work out the values of x=\pm 1 on the cubic and then plug those pairs of results, (x,y) coordinates, into the line equation to see which one works because one of the won't for obvious reasons. Whichever one satisfies the line equation is your point.
    Thankyou!!
 
 
 
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