Final answer:
To find the average rate of change of the function k(x) = -2x^2 over the interval (-3, 6], subtract the function values at the endpoints and divide it by the difference in x-values.
Step-by-step explanation:
To find the average rate of change of the function k(x) = -2x^2 over the interval (-3, 6], we need to find the difference in the function values at the endpoints and divide it by the difference in x-values.
Substituting x = -3 into the function, we get k(-3) = -2(-3)^2 = -2(9) = -18.
Substituting x = 6 into the function, we get k(6) = -2(6)^2 = -2(36) = -72.
Thus, the average rate of change is (-72 - (-18))/(6 - (-3)) = -54/9 = -6.