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