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27 votes
Please please help *image attached* it’s ap calc ab

Please please help *image attached* it’s ap calc ab-example-1
User Laser Hawk
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1 Answer

20 votes
20 votes

The average rate of change of a function f(x) over some interval [a, b] is the difference quotient,


(f(b)-f(a))/(b-a)

which corresponds to the slope of the line connecting the points (a, f(a)) and (b, f(b)) in the graph of f(x).

Given f(x) = 3x² - x³ (correct me if I'm wrong, the exponents look cut off in your screenshot), the average rate of change on [1, 5] is


(f(5)-f(1))/(5-1)=\frac{(3\cdot5^2-5^3)-(3\cdot1^2-1^3)}4 = \frac{75-125-3+1}4 = \boxed{-13}

User David Berry
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