Question

Find the average rate of change of f(x)=3x^2-5 over the interval [1,2].

12
20
25
3
5
10
9
6

Answer 1

9

Explanation:

To find the average rate of change of a function (f(x)) over an interval ([a, b]), you use the formula:Average Rate of Change = (\frac{f(b) - f(a)}{b - a})In this case, (f(x) = 3x^2 - 5), and the interval is ([1, 2]), so (a = 1) and (b = 2). Plugging in the values:Average Rate of Change = (\frac{f(2) - f(1)}{2 - 1} = \frac{(3 \cdot 2^2 - 5) - (3 \cdot 1^2 - 5)}{2 - 1} = \frac{12 - 5 - 3 + 5}{1} = \frac{9}{1} = 9)So, the correct answer is 9.