Final answer:
The average rate of change of the function f(x) = 3x² – 6x from x₁ = –2.4 to x₂ = 1.5 is calculated using the values of the function at these points. It is found to be -8.7 when rounded to the nearest hundredth.
Step-by-step explanation:
The average rate of change of a function f(x) over an interval [x1, x2] is calculated by the difference in function values at these points divided by the difference in x values. This is given by the formula:
Average rate of change = (f(x2) – f(x1)) / (x2 – x1)
For the function f(x) = 3x² – 6x, we need to calculate f(1.5) and f(–2.4) and then use the formula:
f(1.5) = 3(1.5)² – 6(1.5) = 3(2.25) – 9 = 6.75 – 9 = –2.25
f(–2.4) = 3(–2.4)² – 6(–2.4) = 3(5.76) + 14.4 = 17.28 + 14.4 = 31.68
Now, the average rate of change from x1 = –2.4 to x2 = 1.5 is:
(–2.25 – 31.68) / (1.5 - (–2.4)) = (–34.93) / (3.9) = –8.7
Therefore, rounded to the nearest hundredth, the average rate of change of f(x) from x1 = –2.4 to x2 = 1.5 is –8.7.