Two students in your class, Hunter and Maggie, are disputing a function. Hunter says that for the function, between x = -2 and x = 2, the average rate of change is 0. Maggie says that for the function, between x = -2 and x = 2, the graph goes up through a turning point, and then back down. Explain how Hunter and Maggie can both be correct, using complete sentences.

Question

ranga · Answer

The average rate of change of a function over an interval [a,b] is:
{ f(b) - f(a) } / (b-a)  ------ (1)
If Hunter says the average rate of change between [-2,2] is 0 and if he is correct it means f(2) = f(-2) and so the numerator in equation (1) is zero.

If a continuous function has the same value of zero at tow points, then it must take a turn somewhere in between.  The graph lists the two possibilities:|dw:1387918469983:dw|