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**david18** Given that $\displaystyle y= \frac{1}{3}x^{3}-9x $

This part asks me to differentiate the equation and find the minimum and maximums, but I did all that, byt the next part got me:

Given that $\displaystyle 24x+3y+2=0 $ is the equation of the tangent to the curve at the point (p,q) , find p and q.

Now I got the answer to be (1,-22/3) and (-1, 26/3)

But theres only one answer which is (1,-22/3) and the other one isn't mentioned in the answer book. I know that the tangent is only hitting the curve at one point, but what can help me decide between the two? (by the way I used the method where I found what values of x made the derivative = -8, rather than solving the 2 simultaneously because Im bad at factorising cubics.)