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Find the average rate of change of $f(x) = x - 4$ 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

f(x) = x - 4

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

.

Calculate $f(5)$ values: To find the average rate of change, we need to calculate the difference in function values divided by the difference in $x$ values. $\newline$ Calculate $f(5)$ and $f(5 + h)$ : $\newline$ $f(5) = 5 - 4 = 1$ $\newline$ $f(5 + h) = (5 + h) - 4 = 1 + h$
Find difference in function values: Now, find the difference in function values: $f(5 + h) - f(5) = (1 + h) - 1 = h$
Calculate difference in x values: Calculate the difference in x values: $\newline$ egin{equation}( $5$ + h) - $5$ = h $\newline$ egin{equation}
Divide to find average rate: Now, divide the difference in function values by the difference in x values to find the average rate of change: $\newline$ Average rate of change = $\frac{h}{h} = 1$

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