Find the average rate of change of f(x) = -3x^2 - 5x from x = 3 to x = 6.
Simplify your answer as much as possible.
To find the average rate of change of a function from x = a to x = b, we use the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
In this case, a = 3 and b = 6, so:
f(3) = -3(3)^2 - 5(3) = -27 - 15 = -42
f(6) = -3(6)^2 - 5(6) = -108 - 30 = -138
Average rate of change = (-138 - (-42)) / (6 - 3)
= (-138 + 42) / 3
= -96 / 3
= -32
Therefore, the average rate of change of f(x) = -3x^2 - 5x from x = 3 to x = 6 is -32.