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Find the average rate of change of $g(x) = 9x^2 + 14$ between $x = 0$ and $x = h$ , 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) = 9x^2 + 14

between

x = 0

and

x = 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 $x = 0$ and $x = h$ . $\newline$ $g(0) = 9(0)^2 + 14 = 14$ $\newline$ $g(h) = 9(h)^2 + 14$
Find change: Find the change in $g(x)$ over the change in $x$ .
Change in $g(x)$ = $g(h) - g(0) = (9h^2 + 14) - 14 = 9h^2$
Change in $x$ = $h - 0 = h$
Calculate average rate: Calculate the average rate of change. $\newline$ Average rate of change = $(\text{Change in } g(x)) / (\text{Change in } x) = \frac{9h^2}{h} = 9h$

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