Question

1. if $f(x)=-x^{2}+4x - 3$, what is the average rate of change over $0,2$?

a. 0
b. -2
c. 1
d. 2

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\), \(b=2\), and \(f(x)=-x^{2}+4x - 3\).

Step2: Calculate \(f(0)\) and \(f(2)\)

• For \(x = 0\):

\(f(0)=-(0)^{2}+4(0)-3=- 3\)

• For \(x = 2\):

\(f(2)=-(2)^{2}+4(2)-3=-4 + 8-3=1\)

Step3: Substitute into the average - rate - of - change formula

\(\frac{f(2)-f(0)}{2 - 0}=\frac{1-(-3)}{2}=\frac{1 + 3}{2}=\frac{4}{2}=2\)

Answer:

d. 2