Final answer:
The average rate of change of f(x)=-3x^2-x from x1=5 to x2=6 is -34.
Step-by-step explanation:
The average rate of change of a function is determined by finding the difference in the function values at the two given points and dividing by the difference in the x-values. In this case, we have:
f(5) = -3(5)^2 - 5 = -75 - 5 = -80
f(6) = -3(6)^2 - 6 = -108 - 6 = -114
The average rate of change is then:
(f(6) - f(5))/(6 - 5) = (-114 - (-80))/(6 - 5) = -34
Therefore, the average rate of change of f(x)=-3x^2-x from x1=5 to x2=6 is -34.