if ( f(x)=-x^{2}+2 x+3 ), what is the average rate of change over ( 0,3 ) ?
if ( f(x)=-x^{2}+2 x+3 ), what is the average rate of change over ( 0,3 ) ?
Answer
Explanation:
Step1: Recall the formula for average rate of change
The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 0), (b=3), and (f(x)=-x^{2}+2x + 3).
Step2: Calculate (f(0)) and (f(3))
- For (x = 0): (f(0)=-(0)^{2}+2(0)+3=3).
- For (x = 3): (f(3)=-(3)^{2}+2(3)+3=-9 + 6+3=0).
Step3: Substitute into the formula
(\frac{f(3)-f(0)}{3 - 0}=\frac{0 - 3}{3}=\frac{-3}{3}=-1).
Answer:
b. -1