Question

f(x) = $x^2$+2x+5. Find the average rate of change of f(x) in the interval [0,2]

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Answer 1

The average rate of change of a function f(x) with respect to x over an interval [a, a+h] is defined as $\frac{f(a+h)-f\left(a\right)}{h}$. We will first find the initial and final values of f(x) in the given interval, then the change/difference. We will take the ratio of this change with the change in x to get the average rate of change.

f(0) = 0+0+5 = 5

f(2) = 4+4+5 = 13

Change in f(x) = 13-5 = 8

Change in x = 2-0 = 2

Ratio = $\frac{f(a+h)-f\left(a\right)}{h}$=$\frac{8}{2}$ = 4