1. Derivatives and Slopes:Goal: identify tangent lines to a graphUse limits to find slope Use limits to find derivatives Tangent Line to a Graph: The slope of the line tangent to a curve at a given point determines the rate at which the graph rises or falls at that given point. http://www.ies.co.jp/math/java/calc/index.html
3. Slope and limit:Just looking at the graph can be difficult and inaccurate. Secant line recall from geometry a secant is a line that passes through two points on a circle.
11. Going back to the original coordinates for the secant line: (x + Δx, f(x + Δx) f(x + Δx) – f(x) (x, f(x)) Δx Slope = m = f(x + Δx) – f(x) Difference Quotient Δx
12. Definition of the Slope of a Graph: The slope m of the graph of ƒ at the point (x, ƒ(x)) is equal to the slope of its tangent line at (x, ƒ(x)), and is given by msec = m = Provided this limit exists.