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Find the average rate of change of $f(x) = -2x$ between $x = -3$ and $x = -3 + h$ , 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 II

Full solution

Q. Find the average rate of change of

f(x) = -2x

between

x = -3

and

x = -3 + 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 $x = -3$ . $\newline$ $f(-3) = -2(-3) = 6$
Calculate $f(x + h)$ : Calculate $f(x)$ at $x = -3 + h$ . $\newline$ $f(-3 + h) = -2(-3 + h) = 6 - 2h$
Find average rate of change: Find the average rate of change from $x = -3$ to $x = -3 + h$ . $\newline$ Average rate of change = $\frac{f(-3 + h) - f(-3)}{(-3 + h) - (-3)}$ $\newline$ = $\frac{(6 - 2h - 6)}{h}$ $\newline$ = $\frac{-2h}{h}$ $\newline$ = $-2$

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