Calculate, estimate, and interpret average rate of change over an interval.
Calculate the average rate of change of a function on an interval
Problem
Calculate the average rate of change of \(f(x)=x^2\) over \([1,4]\).
Big Picture
What this problem is really about
When a function rule is given, the interval endpoints provide the two inputs for a secant slope. We’ll evaluate the rule at each endpoint first, then divide the difference in those outputs by the difference in the corresponding inputs. Keeping evaluation separate from subtraction prevents an endpoint or an input change from being mistaken for the rate itself.
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