What is the average rate of change of y = cos(2x) on the interval 0, pi/2

Solution:

Given, the function is y = cos(2x)

We have to find the average rate of change of the given function on the interval 0, pi/2.

The average rate of change of a function f(x) over an interval [a, b] is given by

A = [f(b) - f(a)]/(b - a)

Here, a = 0 and b = π/2

f(x) = cos(2x)

Now, f(a) = f(0) = cos(2.0)

= cos(0)

= 1

f(b) = f(π/2) = cos(2.π/2)

= cos(π)

= -1

Now, A = [-1 - 1]/(π/2 - 0)

= (-2)/π/2

= -4/π

Therefore, the average rate of change of the function is -4/π.

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What is the average rate of change of y = cos(2x) on the interval 0, pi/2

Summary:

The average rate of change of y = cos(2x) on the interval 0, pi/2 is -4/π.