Answer:
The average rate of change in the interval (3, 3.5) is -158.75
Step-by-step explanation:
We are given the following function in the question:
[tex]f(x) = -5x^3[/tex]
We have to find average rate of change over the interval:
x = 3 to x = 3.5
Average rate of change =
[tex]=\dfrac{\delta f(x)}{\delta x}\\\\=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\\\\=\dfrac{-5(3.5)^3+5(3)^3}{3.5-3}\\\\= \dfrac{-79.375}{0.5}\\\\=-158.75[/tex]
Thus, the average rate of change in the interval (3, 3.5) is -158.75
