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25 March, 09:25

What is the average rate of change of the function f (x) = 2x2 + x + 5 over the interval - 2 ≤ x ≤ 2?

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  1. 25 March, 11:58
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    16

    Step-by-step explanation:

    Given the function f (x) = 2x² + x + 5, the rate of change of the function is given as d{f (x) }/dx = 4x+1

    Expressing the rate of change over an interval - 2 ≤ x ≤ 2:

    When x = - 2

    d{f (x) }/dx = 4 (-2) + 1

    d{f (x) }/dx = - 8+1

    d{f (x) }/dx = - 7

    When x = 2

    d{f (x) }/dx = 4 (2) + 1

    d{f (x) }/dx = 8+1

    d{f (x) }/dx = 9

    Average rate of change = 9 - (-7)

    Average rate of change = 16
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