Question

Calculate the average rate of change of f(x) = x2 4 - 5 for 3 ≤ x ≤ 5. A) -2 B) - 4 3 C) 4 3 D) 2

Answer 1

D)2

Explanation:

ƒ(x) = x²/4 - 5; 3 ≤ x ≤ 5

Calculate the values of f(3) and f(5)

f(3) = 3²/4 - 5 = 9/4 - 5 = -2.75

f(5) = 5²/4 - 6 = 25/4 - 5 = 1.25

Calculate the average rate of change

Rate of change = (y₂ - y₁)/(x₂-x₁) = [1.25 -(-2.75)]/(5 - 3) = 4.00/2

= 2.00

The average rate of change is 2.00.

In the figure below, the red curve represents the function ƒ(x), while the black dashed line represents the average rate of change over the interval (3, 5).

The value of ƒ(x) increases by two units for every unit that x increases.