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

D) 2

Step-by-step 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.