Answer:
Rate of change = -1
Step-by-step explanation:
Given:
f(x) = -½(x + 2)² + 5
Required:
Average rate of change from x = -3 to x = 1
Solution:
Rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
Where,
a = -3,
f(a) = f(-3) = -½(-3 + 2)² + 5 = -½(-1)² + 5 = 4.5
b = 1,
f(b) = f(1) = -½(1 + 2)² + 5 = -½(9) + 5 = 0.5
Plug in the values into the formula:
Rate of change = [tex] \frac{0.5 - 4.5}{1 - (-3)} [/tex]
Rate of change = [tex] \frac{-4}{4} [/tex]
Rate of change = -1
