The Slope of a Curve

The slope of a line is easy. What about a curve though? To think about it, you could say the slope of a linear function, m, can be interpreted as a rate of change. The change in y, over the change in x. Here we come up with the solution. The line TANGENT to the curve at a point is the straight line that most closely resembles the curve at that given point.

Here we can begin using this equation shown below..

This gives you the slope of a curve, m, at a given point (x_0,f(x_0)), notice that we are now using f(x_0) as y_0, and f(x) instead of y in general.

Your first step in determining the slope of a curve, is to use that expression. You must know certain things though, such as the point x_0.
After having done that, simplify the expression and try to factor h out of all the terms, so that you're able to get rid of the h variable as much as you can.
Now, substitute 0 in for h, and evaluate, this will then give you the slope of the tangent to the curve, and thus, the slope of the curve at that certain point.