Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary interval [a , b] is equal to the instantaneous rate of change of f at the midpoint of that interval. Show and explain your work. (Note: This will be true for any quadratic function, and not just for the given one.)
Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary interval [a , b] is equal to the instantaneous rate of change of f at the midpoint of that interval. Show and explain your work. (Note: This will be true for any quadratic function, and not just for the given one.)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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