Calculate, estimate, and interpret average rate of change for quadratic functions.
Find the average rate of change of a quadratic function on an interval
Problem
Find the average rate of change of \(f(x)=x^2\) over \([1,4]\).
Big Picture
What this problem is really about
For a quadratic, the interval endpoints first have to be turned into points on the function. We’ll evaluate those two outputs, form a consistent difference quotient, and connect the calculation to the rise and run of the secant through the endpoint points.
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