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The average rate of change of a function is the slope of the function
The average rate of change over the interval 2 < x ≤ 4 is 2
The function is given as:
[tex]f(x) = 2x + 10[/tex]
The interval is given as: 2 < x ≤ 4
Start by calculating f(2) and f(4)
[tex]f(2) = 2*2 + 10= 14[/tex]
[tex]f(4) = 2*4 + 10= 18[/tex]
The average rate is then calculated as:
[tex]m = \frac{f(4) -f(2)}{4 -2}[/tex]
This gives
[tex]m = \frac{18 - 14}{2}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m =2[/tex]
Hence, the average rate of change over the interval 2 < x ≤ 4 is 2
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