Calculate, estimate, and interpret average rate of change for quadratic functions.
Decide whether the average rate of change of a quadratic on an interval is positive, negative, or zero
Problem
Is the average rate of change of \(f(x)=x^2\) over \([-2,2]\) positive, negative, or zero?
Big Picture
What this problem is really about
The sign of an average rate depends on the net change between the endpoint outputs, not on every turn the graph makes inside the interval. We’ll evaluate both endpoints carefully, compare their heights over a nonzero horizontal run, and use the resulting secant direction to classify the rate.
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