91Ó°ÊÓ

Consider the function$f\left(x\right)=8x^2-x$.

Now the function value for $x=1$is given as

role="math" localid="1645936319874" $$\begin{gathered} f\left(1\right)=8×1^2-1 \\ f\left(1\right)=8×1-1 \\ f\left(1\right)=8-1 \\ f\left(1\right)=7 \end{gathered}$$

Again, the function value for $x=2$is given as

role="math" localid="1645936422077" $$\begin{gathered} f\left(2\right)=8×2^2-2 \\ f\left(2\right)=8×4-2 \\ f\left(2\right)=32-2 \\ f\left(2\right)=30 \end{gathered}$$

The average of change for the function $f\left(x\right)$from $1$to $2$is given as

$\begin{array}{rcl}\frac{f\left(2\right)-f\left(1\right)}{2-1}& =& \frac{30-7}{1}\\ & =& 23\end{array}$

Consider the function$f\left(x\right)=8x^2-x$.

Now the function value for $x=0$is given as

$$\begin{gathered} f\left(0\right)=8×0^2-0 \\ f\left(0\right)=0 \end{gathered}$$

Again, the function value for $x=1$is given as

$$\begin{gathered} f\left(1\right)=8×1^2-1 \\ f\left(1\right)=8×1-1 \\ f\left(1\right)=8-1 \\ f\left(1\right)=7 \end{gathered}$$

The average of change for the function $f\left(x\right)$from $0$to $1$is given as

$\begin{array}{rcl}\frac{f\left(1\right)-f\left(0\right)}{1-0}& =& \frac{7-0}{1}\\ & =& 7\end{array}$

Consider the function$f\left(x\right)=8x^2-x$.

Now the function value for $x=2$is given as

$$\begin{gathered} f\left(2\right)=8×2^2-2 \\ f\left(2\right)=8×4-2 \\ f\left(2\right)=32-2 \\ f\left(2\right)=30 \end{gathered}$$

Again, the function value for $x=4$is given as

$$\begin{gathered} f\left(4\right)=8×4^2-4 \\ f\left(4\right)=8×16-4 \\ f\left(4\right)=128-4 \\ f\left(4\right)=124 \end{gathered}$$

The average of change for the function $f\left(x\right)$from $2$to $4$is given as

$\begin{array}{rcl}\frac{f\left(4\right)-f\left(2\right)}{4-2}& =& \frac{124-30}{2}\\ & =& \frac{94}{2}\\ & =& 47\end{array}$