Question

Find the average rate of change of g(x) = -x² over the interval (-9, -4]. Write your answer as an integer, fraction, or decimal rounded to the nearest tenth.

Answer 1

The average rate of change of g(x) = -x² over the interval (-9, -4] is found by calculating the function's value at both endpoints and dividing the difference by the length of the interval, which results in 13.

Step-by-step explanation:

To find the average rate of change of a function over a specific interval, you subtract the function's values at the end of the interval from the function's values at the beginning of the interval and divide by the length of the interval. In this case, we're working with the function g(x) = -x² over the interval (-9, -4].

• Calculate g(-9): g(-9) = -(-9)² = -81.
• Calculate g(-4): g(-4) = -(-4)² = -16.
• The change in g(x) is g(-4) - g(-9) = -16 - (-81) = 65.
• The change in x is -4 - (-9) = 5.
• The average rate of change is 65 / 5 = 13.

The average rate of change of g(x) over the interval (-9, -4] is 13.