Question

1. determine the average rate of change of f(x) = 3x² - 4x + 5 over the interval -3,1

f(1)=

f(-3)=

the average rate of change is

show your work

Explanation:

Step1: Calculate f(1)

Substitute x=1 into f(x):
$f(1)=3(1)^2 -4(1)+5=3-4+5=4$

Step2: Calculate f(-3)

Substitute x=-3 into f(x):
$f(-3)=3(-3)^2 -4(-3)+5=27+12+5=44$

Step3: Compute average rate of change

Use formula $\frac{f(b)-f(a)}{b-a}$ with a=-3, b=1:
$\frac{4-44}{1-(-3)}=\frac{-40}{4}=-10$

Answer:

f(1)=4
f(-3)=44
The average rate of change is -10