Given that

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

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.)