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

The average rate of change for the given function on the interval -4 <= x <= 0 is -2.

Step-by-step explanation:

The function can be defined by the equation = 2ଶ 5 − 6. To find the average rate of change for this function on the interval −4 ≤ ≤ 0, we need to find the difference in the function values at the endpoints of the interval and divide it by the difference in the input values:

average rate of change = (f(0) - f(-4))/((0) - (-4))

Substituting the given function, we have:

average rate of change = (2(0)^2 + 5(0) - 6 - (2(-4)^2 + 5(-4) - 6))/((0) - (-4))

Simplifying the expression in the numerator gives:

average rate of change = (-32 - 20 + 6 - (32 - 20 - 6))/((0) - (-4))

Continuing to simplify the expression, we get:

average rate of change = (-32 - 20 + 6 - 32 + 20 + 6)/((0) - (-4))

Finally, calculating the final expression gives:

average rate of change = -8/4 = -2