I have to find the coordinates of the point of intersection of the tangents to the graph of y=x^2 at the points at which it meets the line with equation y=x+2.
This is what I have so far:
y=x^2 intersects with y=x+2 at -1 or 2 since x^2=x+2 factorises to (x+1)(x-2)
The derivative of y=x^2 is 2x , so the gradients of y=x^2 at these points are -2 and 4
I am stuck on where to proceed from here, could somebody please nudge me in the right direction?