find the average rate of change of f(x)= - 3x...
find the average rate of change of f(x)= - 3x^2 + 4 from x = 3 to x = 7. simplify your answer as much as possible.
Answer
# Explanation:
## Step1: Encontrar f(3)
Sustituir x = 3 en f(x)=-3x² + 4.
$f(3)=-3(3)^{2}+4=-3\times9 + 4=-27 + 4=-23$
## Step2: Encontrar f(7)
Sustituir x = 7 en f(x)=-3x² + 4.
$f(7)=-3(7)^{2}+4=-3\times49+4=-147 + 4=-143$
## Step3: Aplicar la fórmula de tasa de cambio promedio
La fórmula de tasa de cambio promedio de una función f(x) de x = a a x = b es $\frac{f(b)-f(a)}{b - a}$. Aquí, a = 3, b = 7.
$\frac{f(7)-f(3)}{7 - 3}=\frac{-143-(-23)}{4}=\frac{-143 + 23}{4}=\frac{-120}{4}=-30$
# Answer:
-30