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Q39.

Expert-verifiedFound in: Page 157

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Find the net change in the value of function $f\left(x\right)=3x-2$ for the inputs from $x=1\mathrm{to}x=5$.**

The net change in the value of function is $f\left(5\right)-f\left(1\right)=12$.

From the given function,

$f\left(x\right)=3x-2....\left(1\right)$

Evaluate $f\left(1\right)\text{and}f\left(5\right)$ gives,

role="math" localid="1644528261712" $f\left(1\right)=3\left(1\right)-\mathrm{2....}\left(\text{Substitute}x=1\text{in}\left(1\right)\right)\phantom{\rule{0ex}{0ex}}=1\phantom{\rule{0ex}{0ex}}f\left(5\right)=3\left(5\right)-2....\left(\text{Substitute}x=5\text{in}\left(1\right)\right)\phantom{\rule{0ex}{0ex}}=13$

Evaluate difference at extreme points gives the net change $f\left(b\right)-f\left(a\right)$ where role="math" localid="1644528485437" $b>a$. Therefore,

$\begin{array}{c}f\left(5\right)-f\left(1\right)=13-1\\ =12\end{array}$

The net change in the value of function is $f\left(5\right)-f\left(1\right)=12$.

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