Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

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Find the average rate of change of $f\left(x\right)=3x-5$ from $x=0 tp x=4$

Step-by-Step Solution

Answer

The average rate of change of $f\left(x\right)=3x-5$ from $x=0 to x=4$ is $3$

Step 1. Given

The function $f\left(x\right)=3x-5$

From $x=0 to x=4$

To find the average rate of change.

Step 2. Find the function at given points.

At $x=4,$

$$\begin{gathered} f\left(4\right)=3\left(4\right)-5 \\ =12-5 \\ =7 \end{gathered}$$

$$\begin{gathered} f\left(0\right)=3\left(0\right)-5 \\ =-5 \end{gathered}$$

Step 3. Average rate of change

Average rate of change$=\frac{f\left(b\right)-f\left(a\right)}{b-a},b\ne a$

Step 4. Substitute the values in the formula.

Substitute the given values in the formula,

Rate of change $=\frac{f\left(4\right)-f\left(0\right)}{4-0},4\ne 0$    $$\begin{gathered} =\frac{7-(-5)}{4-0} \\ =\frac{12}{4} \\ =3 \end{gathered}$$