I'm given f(x) = x^2 and g(x) = -x^2 + 2x - 5 And it says Let A (a, f(a)) be the point of tangency on f(x) and B (b, g(b)) be the point of tangency on g(x). Use calculus to find the slope of the tangent line at each point. What must be true about these two slope expressions? I know we need to use the derivatives, but do I use the original form of the derivative f(x + deltax) - f(x)/delta x or the alternate form f(x) - f(c)/x-c? I would think to use the alternate form, because it gives us points of tangency... but when I try to use the alternate form on g(x), I can't seem to get an answer. For f(x): x^2 - a^2 / (x-a) (x+a)(x-a) / (x-a) = x+a I think I did that right. Now for g(x): -x^2+2x-5+b^2-2b+5/ (x-b) -x^2 + 2x + b^2 - 2b/ (x-b) And I'm basically stuck on what to do from here. Any ideas? Or am I supposed to be using the other derivative equation?