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?

Answer 1

To find the average rate of change of the function f(x) = 2x² + 5x - 6 from x = -4 to x = 0, evaluate the function at both ends and divide the difference by the interval length.

Step-by-step explanation:

The question asks about finding the average rate of change of a quadratic function, specifically f(x) = 2x² + 5x - 6, on a given interval from x = -4 to x = 0. To compute this, one needs to evaluate the function at both endpoints of the interval and then apply the formula for the average rate of change which is given by (f(b) - f(a)) / (b - a), where 'a' and 'b' are the endpoints of the interval.

Steps to Calculate the Average Rate of Change:

First, we evaluate the function at the lower bound of the interval: f(-4) = 2(-4)² + 5(-4) - 6.

Next, we find the value of the function at the upper bound of the interval: f(0) = 2(0)² + 5(0) - 6.

Then, we subtract f(a) from f(b), and divide by the interval length (b - a) to get the average rate of change: (f(0) - f(-4)) / (0 - (-4)).