These exercises investigate the relationship between polynomial functions and their average rates of change. For example, the

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These exercises investigate the relationship between polynomial functions and their average rates of change. For example, the average rate of change of f(x) = x2 from x to x + 0.001 for any x can be calculated and graphed as shown in the figures. The graph of f is a parabola, and the graph of its average rate of change is a line. Try to discover what this relation- ship is by completing the following.image


(a) Graph each function and its average rate of change from x to x + 0.001. 


(b) Compare the graphs. How are turning points on the graph of a function related to its average rate of change? 


(c) Generalize your results. Test your generalization.image

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