Suppose that $f(x) = 8 - 3x$. (a) Determine the average rate of change of $f$ between $x = 0$ and $x = 2$ and the average rate of change of $f$ between $x = 15$ and $x = 50$ (b) Were the two average rates of change that you found in part(a) the same? Explain why or why not.
Recall that the formula for averate rate is...
$\displaystyle \frac{f(b) - f(a)}{b - a}$
Thus,
$
\begin{equation}
\begin{aligned}
\text{a.) } \frac{f(2) - f(0)}{2 - 0} &= \frac{8-3(2) - [8-3(0)]}{2}\\
\\
&= \frac{8-6-8}{2}\\
\\
&= -3
\\
\\
\\
\frac{f(50) - f(15)}{50-15} &= \frac{8-3(50) - [ 8 - 3 (15) ] }{35}\\
\\
&= \frac{8-150-8+45}{35}\\
\\
&= \frac{-105}{35}\\
\\
&= -3
\end{aligned}
\end{equation}
$
b.) The average rates are the same in part(a). This shows that the distance covered between the two pair of points have equal slopes.
Sunday, November 22, 2015
College Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 62
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