Question

find the average rate of change of f(x) = x³ - 7x + 1 over the following intervals.
(a) from -7 to -6
(b) from -5 to 2
(c) from 2 to 8

(a)the average rate of change from -7 to -6 is 120.
(b) the average rate of change from -5 to 2 is \boxed{}

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) over the interval \([a, b]\) is given by \(\frac{f(b) - f(a)}{b - a}\).

Step2: Calculate \( f(-5) \)

Given \( f(x)=x^{3}-7x + 1 \), substitute \( x=-5 \):

$$
LATEXBLOCK0
$$

Step3: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) \):

$$
LATEXBLOCK1
$$

Step4: Apply the average rate of change formula

Here, \( a=-5 \), \( b = 2 \). So,

$$
LATEXBLOCK2
$$

Answer:

12