Question

What is the average rate of change of the function f(x) = 5x ^ 2 + 20x between x = 0 and x = 0.5

Answer 1

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Answer:

22.5

Explanation:

The average rate of change on the interval [a, b] is the ratio ...

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

For your function and interval, it is ...

(f(0.5) -f(0))/(0.5 -0)

Since f(0) = 0, this reduces to ...

average rate of change = 2·f(0.5) = 2(5(0.5)² +20(0.5)) = 2(5/4 +10)

average rate of change = 22.5