given the secant line with points x and x+h, the tangent at x is the line that results as h approaches 0
the limit of the difference quotient in terms of x and h can be used to find the derivative with respect to x
geometric interpretation of the derivative: f'(x) is the function whose value at x is the slope of the tangent line to f at x
to find the tangent line equation, you can simply find the derivative, a set of points on the original function, and the point-slope formula