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Find the average rate of change of $g(x) = x + 14$ between $x = 5$ and $x = 5 + h$ , 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 + 14

between

x = 5

and

x = 5 + h

, where

h \neq 0

.

\newline

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

h

.

Identify function and points: Identify the function and the points for calculating the average rate of change. $\newline$ $g(x) = x + 14$ $\newline$ Points: $x = 5$ and $x = 5 + h$
Calculate function values: Calculate the function values at these points. $\newline$ $g(5) = 5 + 14 = 19$ $\newline$ $g(5 + h) = (5 + h) + 14 = 19 + h$
Use average rate of change formula: Use the formula for average rate of change: $(g(x_2) - g(x_1)) / (x_2 - x_1)$ . Here, $x_1 = 5$ and $x_2 = 5 + h$ . Average rate of change = $(g(5 + h) - g(5)) / ((5 + h) - 5)$ = $(19 + h - 19) / h$ = $h / h$
Simplify expression: Simplify the expression. $\frac{h}{h} = 1$

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