Question

The function () can be defined by the equation () = 2ଶ 5 − 6. What is the average rate of change for this function on the interval −4 ≤ ≤ 0? A. -12 B. -3 C. 3 D. 4

Answer 1

The average rate of change for the function on the interval -4 ≤ x ≤ 0 is -13. None of the options is correct.

Step-by-step explanation:

To find the average rate of change for the function on the interval -4 ≤ x ≤ 0, we need to calculate the change in the function's value over this interval, and then divide it by the change in x. The function is given by f(x) = 2x^2 - 5x - 6.

First, we find the difference in the function's value at the endpoints of the interval: f(0) - f(-4).

Substituting x = 0 into the function, we have f(0) = 2(0)^2 - 5(0) - 6 = -6.

Substituting x = -4 into the function, we have f(-4) = 2(-4)^2 - 5(-4) - 6 = 2(16) + 20 - 6 = 32 + 20 - 6 = 46.

Therefore, the change in the function's value is -6 - 46 = -52.

Next, we find the difference in x: 0 - (-4) = 4.

Finally, we divide the change in the function's value by the change in x: -52/4 = -13.

So, the average rate of change for the function on the interval -4 ≤ x ≤ 0 is -13.