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?

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

On the interval [7π/4, 9π/4], the average slope is

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

Answerthe simplified expression isexplanationthe given expression is,let us deal with the bracket first.the two negatives in the parenthesis will become positive.the expression now becomes,we now expand the parenthesis to get,we group like terms to obtain,this simplifies to,