How do you estimate the rate at a single point on a curve?

For rate I assume you mean gradient. Draw a tangent at the required point. Draw the tangent as long as possible. Measure how high the tangent slope goes in y and how far left or right it goes in x. Then the gradient =this change in y divided by the change in x.

First draw a tangent to the curve at that point. Then find the gradient of that tangent. Typically you would find the gradient by forming a triangle with the line using points with whole number co-ordinates to make life easier. Then the gradient will be the change in the y direction divided by the change in the x direction. If the line is like / it will have a positive gradient and if it is like \ it will have a negative gradient.