Question

What is the rate of change between the interval of x = 3 pi over 2 and x = 2π?

Answer 1

Check the picture below.

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ \begin{cases} x_1=\frac{3\pi }{2}\\ x_2=2\pi \end{cases}\implies \cfrac{f(2\pi )-f\left( \frac{3\pi }{2} \right)}{2\pi -\frac{3\pi }{2} }\implies \cfrac{3-1}{\frac{4\pi -3\pi }{2}}\implies \cfrac{2}{\quad \frac{\pi}{2}\quad }\implies \cfrac{4}{\pi }$

Answer 2

Answer:

The answer is 4/pi