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.

Hint: a line satisfying the "point-slope form" equation $(y-y_0)=m(x-x_0)$ goes through point $(x_0,y_0)$ and has slope $m$.  In the case of our tangent line, 
$$x_0=1 \\
y_0=f(x_0)=f(1)$$ and $$m=f'(1)=-1$$ (as you correctly computed).
Now that you have the two curves, set them equal to solve for their intersections.
