How do you find the slope of the tangent line to each curve at the given point?
By differentiating the answer and plugging in the x value along
the curve, you are finding the exact slope of the curve at that
point. In effect, this would be the slope of the tangent line, as a
tangent line only intersects another at one point. To find the
equation of a tangent line to a curve, use the point slope form
(y-y1)=m(x-x1), m being the slope. Use the differential to find the
slope and use the point on the curve to plug in for (x1, y1).