Question

What is the average rate of change of cosx from pi/2 to pi : a) 2/π b) -2/π c) π/2 d) -π/2

Answer 1

The average rate of change of cos(x) from pi/2 to pi is -2/pi.

Step-by-step explanation:

The average rate of change of cos(x) from π/2 to π can be calculated by finding the difference in the values of the function at the two endpoints and dividing it by the change in the x-values:

average rate of change = (cos(π) - cos(π/2)) / (π - π/2)

Since cos(π) = -1 and cos(π/2) = 0, the average rate of change is:

average rate of change = (-1 - 0) / (π - π/2)

This simplifies to -2/π, so the correct answer is option b) -2/π.