Question

Given the function (g(x) = -2x + 6x + 15), determine the average rate of change of the function over the interval (2 < x < 7).

- A) (10)
- B) (8)
- C) (9)
- D) (12)

Answer 1

The average rate of change of the function g(x) over the interval 2 < x < 7 is calculated by taking the difference in the function values at x=7 and x=2, and dividing it by the change in x, resulting in -12.

Step-by-step explanation:

The question asks to determine the average rate of change of the function g(x) = -2x^2 + 6x + 15 over the interval 2 < x < 7. To find the average rate of change, we calculate the difference in the function values at the endpoints of the interval and divide by the difference in the x-values.

First, calculate the function values at the endpoints:

g(2) = -2(2)^2 + 6(2) + 15 = -8 + 12 + 15 = 19

g(7) = -2(7)^2 + 6(7) + 15 = -98 + 42 + 15 = -41

Then, calculate the average rate of change:

\[ \frac{g(7) - g(2)}{7 - 2} = \frac{-41 - 19}{7 - 2} = \frac{-60}{5} = -12 \]

So, the average rate of change of the function over the interval 2 < x < 7 is -12, which corresponds to answer D.