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

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