Question

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

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

Answer 1

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

Step-by-step explanation:

The function given is f(x) = x² - 4, and we want to calculate the average rate of change of this function from x = -5 to x = -2. The average rate of change of a function over an interval [a, b] is the change in the function values over the change in x, which is f(b) - f(a) / b - a. So, we need to compute f(-2) - f(-5) / -2 - (-5).

Apply the function to each x value:

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

Now, compute the average rate of change:

f(-2) - f(-5) / -2 - (-5) = 0 - 21 / -2 + 5 = -21 / 3 = -7

Therefore, the average rate of change of f(x) from -5 to -2 is -7.