Calculus: The tangent line intersects a curve at two points. Find the other point. 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.

Your statement that "This was never taught in class" might astonish your instructor.  But even if not, it is very unreasonable to expect to be required to do only that which someone has shown you how to do.  And this is so close to the beaten path that it's not a good example of something you might not have been shown how to do.
When $x=1$, then $y=2$ so you've got a line passing through $(1,2)$ with slope $-1$.  In earlier courses you learned how to write an equation for that line.
Now you need the point of intersection of the graphs of two equations, $y=−x^3+2x+1$ and one other.  You've probably seen problems like that before, and if not, apply some common sense, and if that doesn't work, then tell us with specificity at what point you ran into difficulty.
