What is the rate of change from x = π to x = 3 pi over 2 ? (6 points)

Choice B) -6/pi




Explanation:

When x = pi, the value of y is y = 0. This is one of the infinitely many x intercepts. So the point (pi,0) is on the curve.

When x = 3pi/2, the value of y is y = -3. The point (3pi/2, -3) is another point on this curve. This point is a local and absolute minimum.

Find the slope of the line going through these two points
(x1,y1) = (pi,0)
(x2,y2) = (3pi/2,-3)

Slope Formula:
m = (y2-y1)/(x2-x1)
m = (-3-0)/(3pi/2-pi)
m = (-3)/(3pi/2-2pi/2)
m = (-3)/(pi/2)
m = (-3/1)/(pi/2)
m = (-3/1)*(2/pi)
m = (-3*2)/(1*pi)
m = -6/pi

The slope of the line through the two points is -6/pi
This means that the average rate of change from x = pi to x = 3pi/2 is -6/pi