Question

Consider the function f ( x ) = − 5 x 3 f(x)=-5x3. Determine the average rate of change (ARoC) of f f over the following intervals of x x. From x = 3 x=3 to x = 3.5 x=3.5.

Answer 1

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:

$f(x) = -5x^3$

We have to find average rate of change over the interval:

x = 3 to x = 3.5

Average rate of change  =

$=\dfrac{\delta f(x)}{\delta x}\\\\=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\\\\=\dfrac{-5(3.5)^3+5(3)^3}{3.5-3}\\\\= \dfrac{-79.375}{0.5}\\\\=-158.75$

Thus, the average rate of change in the interval (3, 3.5) is -158.75