3 - Applications of Differentiation

Abstract

This chapter discusses the applications of differentiation. The derivative of a function is the slope of its graph at each point. Where the derivative is positive, the graph slopes upward. Where the derivative is negative, the graph slopes downward. Where the derivative is zero, the graph is horizontal. This information is of great help in sketching curves. A graph that is either convex or concave stays on the same side of its tangent at each point; the graph touches the tangent line, but does not cross it. A point at which the graph crosses its tangent is called an inflection point. The chapter also discusses rectilinear motion. Rectilinear motion is motion along a straight line. From its study arise two important concepts, velocity and acceleration. Acceleration is the derivative of velocity. It measures the rate of change of velocity during motion. Positive acceleration indicates increasing velocity; negative acceleration indicates decreasing velocity; and zero acceleration indicates constant velocity.