find the average rate of change of g(x)=-x² + 5x + 2 from x = 3 to x = 6. simplify your answer as much as…
find the average rate of change of g(x)=-x² + 5x + 2 from x = 3 to x = 6. simplify your answer as much as possible.
Answer
Explanation:
Step1: Recall the formula
The average - rate - of - change formula is $\frac{g(x_2)-g(x_1)}{x_2 - x_1}$, where $x_1 = 3$ and $x_2=6$.
Step2: Calculate $g(3)$
Substitute $x = 3$ into $g(x)=-x^{2}+5x + 2$: $g(3)=-(3)^{2}+5\times3 + 2=-9 + 15+2=8$.
Step3: Calculate $g(6)$
Substitute $x = 6$ into $g(x)=-x^{2}+5x + 2$: $g(6)=-(6)^{2}+5\times6 + 2=-36+30 + 2=-4$.
Step4: Calculate the average rate of change
Substitute $g(3) = 8$ and $g(6)=-4$ into the formula: $\frac{g(6)-g(3)}{6 - 3}=\frac{-4 - 8}{3}=\frac{-12}{3}=-4$.
Answer:
$-4$