What is the rate of change for f(x) = 4 sin x - 2 on the interval from x = 0 to x = pi over 2?

Solution:

The average rate of change of a function f(x) is equivalent to the slope of the secant line connecting the two points on the function on the interval [a, b]. It can be expressed as:

Average rate of change = [f(b) - f(a)] / b - a

f(π/2) = 4 × sin (π/2) - 2

= 4 × 1 - 2 = 2

f(0) = 4 × sin(0) - 2

= 0 - 2 = - 2

Average rate of change = [f(π/2)-f(0)]/(π/2-0)

= (2+2) / (π / 2 - 0)

=8/ π

The rate of change = 8/ π

What is the rate of change for f(x) = 4 sin x - 2 on the interval from x = 0 to x = pi over 2?

Summary:

The rate of change for the function f(x) = 4 sin x - 2 on the interval from [0, π/ 2] is 8/ π.