Question

Let f(x) = x²-4. What is the average rate of change of f(x) from -5 to -2 ?

A. -7
B. -1/7
C. 7
D. 1/7

Answer 1

The average rate of change of the function f(x) = x² - 4 from x = -5 to x = -2 is A. -7.

Step-by-step explanation:

To calculate the average rate of change of the function f(x) = x² - 4 from x = -5 to x = -2, we use the formula:

average rate of change = ∆f(x) / ∆x = [f(x2) - f(x1)] / (x2 - x1)

Firstly, find the value of f at x = -5 and x = -2.

• f(-5) = (-5)² - 4 = 25 - 4 = 21
• f(-2) = (-2)² - 4 = 4 - 4 = 0

Now, calculate the average rate of change:

∆f(x) = f(-2) - f(-5) = 0 - 21 = -21

∆x = -2 - (-5) = -2 + 5 = 3

average rate of change = ∆f(x) / ∆x = -21 / 3 = -7