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Find the average rate of change of $f(x) = 8x^2 - 19$ 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 II

Full solution

Q. Find the average rate of change of

f(x) = 8x^2 - 19

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 $f(0)$ and $f(h)$ : Calculate $f(0)$ and $f(h)$ to use in the average rate of change formula. $\newline$ $f(0) = 8(0)^2 - 19 = -19$ $\newline$ $f(h) = 8h^2 - 19$
Use average rate of change formula: Use the average rate of change formula: $(f(h) - f(0)) / (h - 0)$ . $\newline$ Average rate of change = $(8h^2 - 19 - (-19)) / h$ $\newline$ = $(8h^2) / h$
Simplify the expression: Simplify the expression. $\newline$ Average rate of change = $8h$

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