Question

What is the rate of change from x = π to x = 2π? trig graph with points at 0, negative 4 and pi over 2, 0 and pi, 4 and 3 pi over 2, 0 and 2 pi, negative 4

Answer 1

The given data is
x   0   π/2   π    (3/2)π   2π
y  -4   0      4     0         -4

The curve that models the data is
y = -4 cos(x)  as shown below.

The rate of change of y from x = π to x = 2π is
$\frac{-4-4}{2 \pi - \pi } =- \frac{8}{ \pi }$

Answer: $- \frac{8}{ \pi }$