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2 February, 13:04

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

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  1. 2 February, 13:40
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    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.
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