Question

1. what is the average rate of change for the function f(x) = x² - 3x + 5 on the interval -1 ≤ x ≤ 4? a. -5 b. 0 c. 1 d. 5 test prep #2 25 minutes

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( f(x) \) on the interval \([a, b]\) is given by \(\frac{f(b) - f(a)}{b - a}\). Here, \( a=-1 \) and \( b = 4 \), and \( f(x)=x^{2}-3x + 5 \).

Step2: Calculate \( f(-1) \)

Substitute \( x=-1 \) into \( f(x) \):

$$
LATEXBLOCK0
$$

Step3: Calculate \( f(4) \)

Substitute \( x = 4 \) into \( f(x) \):

$$
LATEXBLOCK1
$$

Step4: Calculate the average rate of change

Using the formula \(\frac{f(4)-f(-1)}{4-(-1)}\), substitute \( f(4) = 9 \) and \( f(-1)=9 \):

$$ \frac{9 - 9}{4+1}=\frac{0}{5}=0 $$

Answer:

B. 0