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Find the average rate of change of $f(x) = x + 16$ between $x = -2$ and $x = -2 + h$ , where $h \neq 0$ . $\newline$ Simplify your answer. Your answer may be a number or an expression in terms of $h$ .

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Average rate of change I

Full solution

Q. Find the average rate of change of

f(x) = x + 16

between

x = -2

and

x = -2 + h

, where

h \neq 0

.

\newline

Simplify your answer. Your answer may be a number or an expression in terms of

h

.

Calculate $f(x)$ : Calculate $f(x)$ at $x = -2$ . $\newline$ $f(-2) = -2 + 16 = 14$
Calculate $f(x + h)$ : Calculate $f(x)$ at $x = -2 + h$ . $\newline$ $f(-2 + h) = (-2 + h) + 16 = 14 + h$
Find average rate of change: Find the average rate of change using the formula: $(f(x_2) - f(x_1)) / (x_2 - x_1)$ . Here, $x_1 = -2$ and $x_2 = -2 + h$ . Average rate of change = $(f(-2 + h) - f(-2)) / ((-2 + h) - (-2))$ = $(14 + h - 14) / h$ = $h / h$ = $1$

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