Mathematics 1560 Lecture 1: c2s1
Document Summary
The average rate of change of y = f (x) with respect to x over the interval [x1, x2] is. X f (x2) f (x1) x2 x1 f (x1 + h) f (x1) h where h = x2 x1. We now informally de ne the slope of a curve at a point p on the curve. At this stage, the slope of a line is de ned, so we use this as a starting point. We de ne the slope of a curve at a point p as the slope of the line tangent to the curve at point p . To nd this tangent line, we approximate it by lines secant to the curve which pass through point p and another point on the curve, say point q. Since we know two points on the secant line, p and q, we can nd the slope of the secant line.
