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Find the average rate of change of $g(x) = x + 11$ between $x = 4$ and $x = 4 + h$ , 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

g(x) = x + 11

between

x = 4

and

x = 4 + h

, where

h \neq 0

.

\newline

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

h

.

Calculate $g(x)$ : Calculate $g(x)$ at $x = 4$ . $\newline$ $g(4) = 4 + 11 = 15$
Calculate $g(x + h)$ : Calculate $g(x)$ at $x = 4 + h$ . $\newline$ $g(4 + h) = (4 + h) + 11 = 15 + h$
Find average rate of change: Find the average rate of change using the formula: $(g(x_2) - g(x_1)) / (x_2 - x_1)$ . $\newline$ Average rate of change = $(g(4 + h) - g(4)) / ((4 + h) - 4)$ $\newline$ = $(15 + h - 15) / h$ $\newline$ = $h / h$ $\newline$ = $1$

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