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. @iambatman

Answer 1

@Ashleyisakitty

Answer 2

Can anyone help me?

Answer 3

\[avg~~ROC=\frac{ f(3)-f(-3) }{ 3-(-3) }\]
For the average rate of change to be 0, f(3) and f(-3) would have to be the same. If the function is continuous, that can only happen if there is a turning point (maximum or minimum) between -3 and 3.