[Mentor's note: This post does not contain the template for thread-starting posts in the homework forums, because it was moved from another forum.] "If f'(x) gives me the slope of f at some point, why doesn't f'(x)x + b = f(x)?" I have no idea how to answer this. Can you? How about: it is the slope of the tangent line to some point of the function, and that set of tangent lines do not share the same y-intercept b necessarily, so b is not constant.