Question

Find the net change in the value of function$f\left(x\right)=4-5x$ for the inputs from$x=3\mathrm{to}x=5$.

Short answer

The net change in the value of function is $f\left(5\right)-f\left(3\right)=-10$.

Step-by-step solution

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

From the given function,

$f\left(x\right)=4-5x\mathrm{....}\left(1\right)$

Evaluate $f\left(3\right)\text{and}f\left(5\right)$gives,

role="math" localid="1644529205710" $$\begin{gathered} f\left(3\right)=4-5\left(3\right)\mathrm{....}\left(\text{Substitute}x=3\text{in}\left(1\right)\right) \\ =-11 \\ f\left(5\right)=4-5\left(5\right)\mathrm{....}\left(\text{Substitute}x=5\text{in}\left(1\right)\right) \\ =-21 \end{gathered}$$

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 $b>a$. Therefore,

role="math" localid="1644529288903" $$\begin{gathered} f\left(5\right)-f\left(3\right)=-21-\left(-11\right) \\ =-10 \end{gathered}$$

Step 3. Description of steps.

The net change in the value of function is $f\left(5\right)-f\left(3\right)=-10$.