Question

Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = -3 and x = 3, the average rate of change is 0. Karly says that for the function, between x = -3 and x = 3, the graph goes up through a turning point, and then back down. Explain how Tucker and Karly can both be correct, using complete sentences.

Answer 1

average rate of change = the average of the slopes = (+ slope + neg slope)/2

Answer 2

if the numerator is zero, the average rate of change is zero

Answer 3

The rate of change on a position vs time graph is also known as the velocity, if you have a +v for 3 seconds and a -v for 3 seconds, the average of the 2 is zero.

Answer 4

thanks!