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.

(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.

Transcribed Image Text:

Plot1 Plot2 Plot3 \Y₁X^2 Y₂E(Y₁(X+.001)- Y₁(X))/((X+.001) -X) \Y3= Y4= Ys= [-10, 10, 1] by [-10, 10, 1]