Question

Examine the following table, which defines the relationship y= f(x). Then, answer the question.

Over which interval does f(x) have the greatest average rate of change?

Answer 1

The slope of the function is most positive either side of x=0 and x=2π.

On the interval [0, π/4], the average slope is
`(((√(2))/(2)))/(((\pi)/(4))) = (2√(2))/(\pi)`

On the interval [7π/4, 9π/4], the average slope is
`(((√(2))/(2)-(-√(2))/(2)))/(((9\pi)/(4)-(7\pi)/(4)))=(2√(2))/(\pi)`


The average rate of change is highest on the intervals [0, π/4] and [7π/4, 9π/4].