The line tangent to $y = -x^3 + 2x + 1$ when $x = 1$ intersects the curve in another point. Find the coordinates of the other point.
This was never taught in class, and I have a test on this tomorrow. This question came off of my test review worksheet, and I don't understand how to solve it. The answers are on the back, and for this one it says the answer is (-2,5), but I don't understand how to get that.
I did the derivative and substituted 1 for x to get the slope of the line:
$y = -x^3 + 2x + 1$
$y' = -3x^2 + 2$
$y' = -3 + 2$
$y' = -1$
I don't know where to go from here.