DEFINITION Rates of Change and the Tangent line The average rate of change in f on the interval [a, x] is the slope of the correspond ing secant line f(r)-f(a) r- a The instantaneous rate of change in f at x= a is f(x-f(a) tan lim x→ax-al which is also the slope of the tangent line at x=a, provided this limit exists. The tangent line at x a is the unique line through(a, f(a)with slope m an. Its equation is y-f(a)= man(x-a) Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-7Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3 - 7