# Question #8b99b

Jan 10, 2018

The average rate of change is 0.

#### Explanation:

Average rate of change is Algebra I slope.

$f \left(x\right) = 3 \sin \left(\frac{\pi}{2} \cdot x\right) + 7$

Average rate of change for this interval is given by:

$\frac{f \left(6\right) - f \left(4\right)}{6 - 4}$

We can calculate the values of the function:
$f \left(6\right) = 3 \sin \left(\frac{\pi}{2} \cdot 6\right) + 7 = 3 \sin \left(3 \pi\right) + 7 = 3 \left(0\right) + 7 = 7$

$f \left(4\right) = 3 \sin \left(\frac{\pi}{2} \cdot 4\right) + 7 = 3 \sin \left(2 \pi\right) + 7 = 3 \left(0\right) + 7 = 7$

So average rate of change of $f \left(x\right)$ on the interval $4 \le x \le 6$ is:

$\frac{7 - 7}{2} = 0$

Jan 10, 2018

$0$

#### Explanation:

.

Average Rate of Change $= \frac{f \left(b\right) - f \left(a\right)}{b - a}$

$= \frac{3 \sin \left(\frac{\pi}{2} \cdot 6\right) + 7 - 3 \sin \left(\frac{\pi}{2} \cdot 4\right) - 7}{6 - 4} =$

$\frac{3 \sin \left(3 \pi\right) - 3 \sin \left(2 \pi\right)}{2} = \frac{0 - 0}{2} = 0$