Two students in your class, wilson and alexis, are disputing a function. wilson says that for the function, between x = -1 and x = 1, the average rate of change is 0. alexis says that for the function, between x = -1 and x = 1, the graph goes up through a turning point, and then back down. explain how wilson and alexis can both be correct, using complete sentences.

We are given that the Wilson states that for the function f(x), -1≤x≤1 the average rate of change of the function is 0 i.e. .

Now, when we have , this implies that a function assume a critical point -1≤x≤1.

If a function has a critical point, we get that at that point the function either assumes its maximum or minimum value.

On the other hand, Alexis states that for the function f(x), -1≤x≤1 the graph goes up through a turning point and then goes back down.

This gives us that the function has a maximum value in -1≤x≤1 from where the graph changes its position from upward to downward.

So, we see that both Wilson and Alexis are implying that the function f(x) has a maximum value in -1≤x≤1.

Hence, both of them are correct in their statements.

michael scott & dwight schrute

step-by-step explanation:

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