ALTERNATIVE DEFINITION Rates of change and the Tangent Line The average rate of change in f on the interval [a, a+ h] is the slope of the corre sponding secant line f(a+ h-f The instantaneous rate of change inf at x a is f(a+ h-f( man= lim (2) →0 h which is also the slope of the tangent line at x a, provided this limit exists Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-10Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3 - 10