Question

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

Short answer

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

Step-by-step solution

Step 1. Evaluate the value of function at extreme points.

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" $$\begin{gathered} f\left(1\right)=3\left(1\right)-\mathrm{2....}\left(\text{Substitute}x=1\text{in}\left(1\right)\right) \\ =1 \\ f\left(5\right)=3\left(5\right)-2....\left(\text{Substitute}x=5\text{in}\left(1\right)\right) \\ =13 \end{gathered}$$

Step 2. Obtain difference at extreme points.

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,

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

Step 3. Description of steps.

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